DYK, Circuit Judge.

This case involves a suit for declaratory judgment seeking to establish ownership rights in a dental implant system. Plaintiff Jack T. Krauser appeals from the final judgment of the United States District Court for the Southern District of Florida in favor of defendants (BioHorizons, Inc., BioLok International, Inc., and BioHorizons Implant Systems, Inc., collectively, "BHI", formerly Minimatic Implant Technology, Inc. or "Minimatic").1 The district court held that Krauser did not have any ownership rights to the dental implant system manufactured by BHI. Because we hold that we do not have jurisdiction to hear this appeal, we transfer this appeal to the Eleventh Circuit.

BACKGROUND

In late 1987, Krauser, a periodontist, designed a dental implant system. In May 1988, he employed Minimatic, the predecessor of defendant BHI, to produce prototypes of the system. Krauser paid Minimatic $200 to produce drawings and prototypes based on Krauser's initial drawings and work product. At this stage, there was apparently no written agreement governing ownership of the implant system. By March 1991, Minimatic "had successfully formulated implants, attachments, and other products based on [Krauser's work product]." J.A. 1317. To pursue marketing and sale of this system, Minimatic and Krauser entered into a written consulting, collaboration, and royalty agreement (the "1991 Agreement"), which specified that Krauser would develop new products for Minimatic and improve upon the dental implant system, and Minimatic would produce and sell the system and the associated products. The 1991 Agreement stated that the "[d]rawings [of the dental implant system] and 510(k)'s are the property of Minimatic." Under the 1991 Agreement, Krauser was entitled to receive a percentage of the net sales from the dental implant system, among other benefits.

In his role at Minimatic, Krauser allegedly collaborated with Leon Shaw, then President of Minimatic, on the development of dental implant systems. In 1994, Krauser obtained a patent, U.S. Patent No. 5,316,476 (the "Krauser patent"), covering one component of the dental implant system and listing Krauser as the named inventor. In 1995 and 1999, respectively, Minimatic secured two patents covering dental implant systems, U.S. Patent Nos. 5,415,545 and 5,964,766, both naming Shaw as the sole inventor (collectively, the "Shaw patents").

In 1993, Krauser alleged that Minimatic had failed to pay the royalties due under the 1991 Agreement. Krauser sued Minimatic and Shaw for a declaration of ownership rights in state court, and for copyright infringement and infringement of the Krauser patent in federal district court. In 1996, while both suits were pending, Minimatic filed for bankruptcy, and Krauser filed claims in bankruptcy court against Minimatic corresponding to the claims asserted in the pending lawsuits. In May 1996, Minimatic and Krauser reached a settlement to resolve Krauser's outstanding claims (the "May 1996 Agreement"). In the May 1996 Agreement, Minimatic "recognize[d] Krauser's significant individual contribution to the invention and creation of what is today known as the `Minimatic Implant System' in concept, design, design application, ease of installation and overall system requirements." J.A. 206 ¶ 18. Although Minimatic initially moved the bankruptcy court to approve the May 1996 agreement, Minimatic withdrew that motion before the settlement was approved, and the bankruptcy court vacated the agreement.

In October 1996, Minimatic and Krauser entered into a second agreement (the "October 1996 Agreement"). In the October 1996 Agreement, Krauser conditionally granted to Minimatic a 10-year license both to the Krauser patent and to "any and all rights he may have ... [to] the dental implant system currently being manufactured by [Minimatic]." J.A. 813 ¶ 2. If Minimatic complied with the terms of the October 1996 Agreement for the specified ten year term, i.e., by paying Krauser royalties from sales of the dental implant products and fulfilling the attendant audit requirements, all of Krauser's rights to the dental implant system and the Krauser patent would be "unconditionally assigned to [Minimatic]" at the end of the ten years. J.A. 813 ¶ 2. But in the "event of a default by [Minimatic] ..., Krauser's conditional grant of a license [would] automatically terminate." J.A. 813 ¶ 2. In addition, Krauser "[would] have the option ... to institute suit against [Minimatic] for money damages and/or a declaration of his rights in and to the dental implant system currently being manufactured by [Minimatic]." J.A. 819 ¶ 8.

The bankruptcy court approved the October 1996 Agreement and incorporated it into Minimatic's Joint Second Amended Plan of Reorganization in February 1997. Pursuant to this reorganization, Minimatic merged into BioLok in 1997.

Between 2000 and 2003, several patents on dental implant systems issued to BioLok (the "BioLok patents").2 None of these patents listed Krauser as an inventor. In his First Amended Complaint in this action, Krauser alleged that he was entitled to be named an inventor on both the Shaw and BioLok patents.

Although BHI paid Krauser royalties for some years, Krauser alleged that BHI failed to pay the full amount of royalties or submit to the audits required by the October 1996 Agreement. In October 2009, Krauser provided BHI a formal notice of default, with a declaration of Krauser asserting that he had ownership rights in the dental implant system and terminating BHI's license to the same.

In 2010, Krauser sued BHI in Florida state court, seeking a declaration that, among other things, Krauser "is the inventor and owner of the subject matter set forth in all of the Defendants' patents based on [the Krauser] Patent [namely, the Shaw and BioLok patents] ... the subject matter set forth in all of the Defendants' 510(k) registrations based on [the Krauser] Patent, [and] of the Dental Implant System, now commercially known as the BioHorizons Tapered Internal Implant System." J.A. 74-75. The Krauser patent had expired in June 1998 for failure to pay maintenance fees. BHI then removed the case to federal district court based on diversity jurisdiction under 28 U.S.C. § 1332 and patent jurisdiction under 28 U.S.C. § 1338(a) based on Krauser's inventorship claims. After removal, BHI moved to dismiss the case for failure to state a claim. In his response, Krauser "withdr[ew], without prejudice, his claims of inventorship, and ... restrict[ed] his claims to his ownership rights in and to [the Dental Implant System]," and described how his complaint could be amended to include only ownership claims. Thereafter, the district court "granted [Krauser] leave to amend to file a complaint that reflects his representation that his claims for inventorship are withdrawn without prejudice." Krauser v. Biohorizons, Inc., No. 10-80454, 2010 WL 3468481, at *5 (S.D.Fla. Sept. 1, 2010).

Krauser filed his Second Amended Complaint that included only ownership claims (rather than inventorship claims). In 2012, Krauser filed a separate action in the U.S. District Court for the Southern District of Florida, seeking correction of inventorship of the BioLok patents,3 all currently held by Evollution IP Holdings and exclusively licensed to BHI. See Compl. ¶¶ 16, 23, 30, 37, Krauser v. Evollution IP Holdings, Inc., No. 12-80977 (S.D.Fla. Sept. 11, 2012), ECF No. 1.

In July 2012, the district court granted BHI's motion for summary judgment in this case, Krauser v. BioHorizons. First, the district court found that because Krauser was seeking a declaratory judgment of his ownership of the dental implant system, not specific performance, his claim was not barred by the one year Florida statute of limitations on specific performance. On the merits of Krauser's declaratory judgment claim, the district court construed the October 1996 Settlement language "currently being manufactured" to apply only to dental implants being manufactured in October 1996, rather than dental implants manufactured at the time of litigation. Finally, the district court found that Krauser had no ownership rights in dental implant systems or to the 510(k)s manufactured on or before October 1996.

Krauser appealed, initially to the Eleventh Circuit. At the Eleventh Circuit, BHI moved to dismiss the appeal or, in the alternative, to transfer to this court. There were three possible theories supporting BHI's assertion that Krauser's complaint necessarily raised a substantial patent law issue. First, Krauser's original complaint contained a patent law claim of inventorship. Second, BHI argued that even though Krauser had amended the complaint to remove the inventorship claims, it was nonetheless necessary to determine inventorship to adjudicate Krauser's remaining ownership claims. Third, BHI argued that because Krauser's ownership claims, purportedly based on contract law, are allegedly preempted by federal patent law, the Federal Circuit has jurisdiction. The Eleventh Circuit transferred the case to this court in a brief per curiam opinion stating that "[b]ecause the Federal Circuit has exclusive appellate jurisdiction in civil actions `arising under ... any Act of Congress relating to patents,' we transfer this appeal to the Federal Circuit." Krauser v. BioHorizons, Inc., No. 13-11123 (11th Cir. June 20, 2013) (omission in original).

JURISDICTION

Although Krauser asserts that we do not have jurisdiction, he concedes that he would prefer to have this court adjudicate his claims in the interest of conserving judicial resources. BHI asserts that this court has jurisdiction. Nevertheless, "[e]very federal appellate court has a special obligation to satisfy itself ... of its own jurisdiction ... even though the parties are prepared to concede it." Chamberlain Grp., Inc. v. Skylink Techs., Inc., 381 F.3d 1178, 1188 (Fed.Cir.2004) (quoting Bender v. Williamsport Area Sch. Dist., 475 U.S. 534, 541, 106 S.Ct. 1326, 89 L.Ed.2d 501 (1986)) (alteration and omissions in original). "We review issues of jurisdiction de novo." Forrester Env. Servs., Inc. v. Wheelabrator Techs., Inc., 715 F.3d 1329, 1333 (Fed.Cir.2013) (quoting Prasco, LLC v. Medicis Pharm. Corp., 537 F.3d 1329, 1335 (Fed.Cir.2008)).

To support our jurisdiction, BHI makes the same jurisdictional arguments as at the Eleventh Circuit. In addition, it contends that its theories, even if ultimately incorrect, are nonetheless "plausible" and require us to follow the law of the case of our sister circuit.

The law of the case issue was addressed by the Supreme Court in Christianson v. Colt Industries Operating Corp., 486 U.S. 800, 815-19, 108 S.Ct. 2166, 100 L.Ed.2d 811 (1988). The Supreme Court explained that the "law of the case" from a sister circuit could counsel against re-transfer — "transferee courts that feel entirely free to revisit transfer decisions of a coordinate court threaten to send litigants into a vicious cycle of litigation," id. at 816, 108 S.Ct. 2166 — but that law of the case was "not a limit to [the] power" of the transferee court. Id. (quoting Messinger v. Anderson, 225 U.S. 436, 444, 32 S.Ct. 739, 56 L.Ed. 1152 (1912)). "[I]f the transferee court can find the transfer decision plausible, its jurisdictional inquiry is at an end." Id. at 819, 108 S.Ct. 2166. But it held that a transferee court would "not exceed its power in revisiting the jurisdictional issue, and once it conclude[s] that the prior decision was `clearly wrong' it [is] obliged to decline jurisdiction." Id. at 817, 108 S.Ct. 2166.

Here, the Eleventh Circuit has transferred this case to us, and accordingly, the Eleventh Circuit's decision should normally be the law of the case. This is true even though the transferring court had not explained the basis for its decision. Id. at 817, 108 S.Ct. 2166. We conclude, however, that there is no "plausible" basis for this court's jurisdiction.4

I

BHI first argues that we have jurisdiction because Krauser included an inventorship claim in his original complaint. "Federal courts have exclusive jurisdiction over cases `arising under any Act of Congress relating to patents.'" Gunn v. Minton, ___ U.S. ___, 133 S.Ct. 1059, 1062, 185 L.Ed.2d 72 (2013) (quoting 28 U.S.C. § 1338(a)). An action "arises under" patent law when "federal [patent] law creates the cause of action asserted" or when it presents a federal patent issue that is "(1) necessarily raised, (2) actually disputed, (3) substantial, and (4) capable of resolution in federal court without disrupting the federal-state balance approved by Congress." Id. at 1064, 1065; see also Colt, 486 U.S. at 808-09, 108 S.Ct. 2166 ("§ 1338(a) jurisdiction... extend[s] only to those cases in which a well-pleaded complaint establishes either that federal patent law creates the cause of action or that the plaintiff's right to relief necessarily depends on resolution of a substantial question of federal patent law, in that patent law is a necessary element of one of the well-pleaded claims."). It is undisputed that Krauser's First Amended Complaint, with its inventorship claim, as filed in state court, "arose under" federal patent law and was subject to § 1338(a) jurisdiction, and correspondingly, our appellate jurisdiction under 28 U.S.C. § 1295(a)(1). See Bd. of Regents, Univ. of Tex. Sys. v. Nippon Tel. & Tel. Corp., 414 F.3d 1358, 1363 (Fed.Cir.2005) ("[I]ssues of inventorship ... present sufficiently substantial questions of federal patent law to support jurisdiction under section 1338(a).").

But after Krauser's withdrawal without prejudice of his inventorship claims, the Second Amended Complaint did not contain any claims which depended "on resolution of a substantial question of federal patent law." Colt, 486 U.S. at 809, 108 S.Ct. 2166. We have repeatedly held that an amendment to the complaint that dismisses the patent law claims without prejudice, as here, deprives this court of jurisdiction over the case. Gronholz v. Sears, Roebuck & Co., 836 F.2d 515, 518 (Fed.Cir.1987) ("[Plaintiff's] dismissal of the patent claim constituted an amendment of his complaint. That amendment left a complaint which consisted of a single, non-patent claim for unfair competition. Applying the well-pleaded complaint rule to the complaint then remaining, we determine that the present suit does not `arise under' the patent laws for jurisdictional purposes."); see also Chamberlain, 381 F.3d at 1189 ("For the purposes of determining Federal Circuit jurisdiction, we do not differentiate between actual and constructive [i.e., dismissals without prejudice] amendments; both divest us of jurisdiction if they eliminate all issues of patent law."); accord Nilssen v. Motorola, Inc., 203 F.3d 782, 785 (Fed.Cir.2000). Therefore, the existence of inventorship claims in the original complaint does not support our exercise of jurisdiction in this case.

II

Second, although BHI conceded that Krauser had removed his inventorship claims from this case, BHI contends that the well-pleaded complaint rule requires us to consider the issue of patent law inventorship even when adjudicating Krauser's claims of ownership of the Dental Implant System based on the 1991 Agreement, the October 1996 Agreement and a quantum meruit theory. While Krauser's theory of ownership of the dental implant system is not entirely clear, his ownership theories do not rest on a theory of inventorship or require resolution of any issue of patent law. In addition, on appeal to this court, Krauser stated that he had withdrawn his claim in the Second Amended Complaint that "he is the owner of the subject matter set forth in the Defendants' patents." J.A. 273. Therefore, BHI's second jurisdictional theory fails every element of the test described by the Supreme Court in Gunn. The resolution of the inventorship question is neither "necessary" nor "substantial" to the case. A claim of ownership does not necessarily require consideration of patent law inventorship. A state law contract claim or quantum meruit claim may entitle Krauser to royalties from the Dental Implant System even if he is not listed as an "inventor" on the face of the patent. Given that there is no federal issue in this case, an exercise of federal question jurisdiction would certainly disrupt "Congress's intended division of labor between state and federal courts." Gunn, 133 S.Ct. at 1065.

III

BHI further argues that even if Krauser's claims are based in state law, there is federal jurisdiction because Krauser seeks remedies that might be preempted by federal patent law. BHI argues that because Krauser's ownership claims are based on his contribution of the ideas in the dental implant system, these claims are preempted. See, e.g., Ultra-Precision Mfg., Ltd. v. Ford Motor Co., 411 F.3d 1369, 1377-82 (Fed.Cir.2005); Univ. of Colo. Found., Inc. v. Am. Cyanamid Co., 342 F.3d 1298, 1305-08 (Fed.Cir.2003); Waner v. Ford Motor Co., 331 F.3d 851, 856-57 (Fed.Cir.2003). But even if Krauser's ownership claims are preempted, this does not give this court jurisdiction. The Supreme Court addressed this very issue in Metropolitan Life Insurance v. Taylor, 481 U.S. 58, 63, 107 S.Ct. 1542, 95 L.Ed.2d 55 (1987) — finding that because "[f]ederal pre-emption is ordinarily a federal defense to the plaintiff's suit ... it does not appear on the face of a well-pleaded complaint, and, therefore, does not authorize removal to federal court." In Forrester, we applied Metropolitan Life to an analogous situation, finding no federal jurisdiction where plaintiff "[sought] remedies that might be preempted by federal patent law" because federal preemption was only a defense to the plaintiff's suit. 715 F.3d at 1335. Therefore, BHI's third theory does not support our exercise of jurisdiction in this case.

In summary, there is no plausible claim that this court has jurisdiction.

TRANSFERRED TO THE ELEVENTH CIRCUIT

COSTS

Costs to neither party.