This is a pay conversion case. The appellants are ten current or former Federal Aviation Administration air traffic controllers who are seeking to recover pay lost due to the government’s failure to provide them with a two-step pay increase when they transferred to higher level airport facilities. The United States Court of Federal Claims dismissed their complaint for lack of jurisdiction. Although we hold that the trial court had jurisdiction over the claim, we affirm the dismissal because the appellants failed to state a claim for which relief can be granted.
I
This case arises out of the decision of the Federal Aviation Administration (“FAA”) in the early 1990s to privatize many of its control tower operations and a subsequent agreement between the FAA and the air traffic controllers’ union, the National Air Traffic Controllers Association (“NATCA”), to alter the compensation scheme for controllers at the remaining facilities. The present dispute stems from the fact that the new compensation scheme was implemented before the privatization plan had been completed.
The appellants were employed by the FAA as air traffic controllers at facilities designated as “Level 1” towers. The FAA classified control towers by the complexity and volume of their air traffic, ranging from Level 1 (least traffic) to Level 5 (most traffic). All controllers were compensated under the General Schedule (“GS”) system,1 with their pay grade being a function of the level of the facility where they worked. The pay grades ranged from GS-10 for Level 1 controllers to GS-15 for Level 5 controllers. Beginning in 1994, the FAA began to implement a plan to privatize all Level 1 facilities. It offered controllers in those towers the option to transfer to a higher level facility or to retire or resign from federal service. The appellants elected to transfer, and they were scheduled to move to higher level facilities in August 1998.
In March 1998, however, the United States District Court for the Northern District of Ohio ruled that the FAA had failed to conduct the required procedural analysis before initiating the privatization program. See Nat’l Air Traffic Controllers Ass’n v. Sec’y of the Dep’t of Transp., 997 F.Supp. 874, 885 (N.D.Ohio 1998). The effect of the court’s ruling was to temporarily halt the implementation of the privatization plan.
*1373During the period that the privatization plan was halted, the FAA and the NATCA entered into a collective bargaining agreement that established a new compensation scheme for air traffic controllers. The new scheme was referred to as the Air Traffic Controller (“ATC”) system.
The ATC system created a set of “Pay and Reclassification Rules” to replace the grades and steps of the GS system. Under the new scheme, controllers were assigned an ATC level and pay band (akin to GS grade and step levels). The collective bargaining agreement also contained a conversion rule (“Rule 35”) for transferring air traffic controllers at Level 2 through Level 5 facilities from the GS system to the ATC system. It provided a formula for determining a controller’s ATC level and pay band, which was based solely on the controller’s prior GS grade and step. However, Rule 35 did not call for controllers at Level 1 facilities to be transferred into the ATC system, as those towers were still slated for privatization. Instead, the Note to Rule 35 stated that Level 1 facilities would be “treated in accordance with current pay policies with the exception that their base pay will be increased by 5% in. the first year.”
The ATC pay scheme took effect in October 1998. Controllers at Level 2 through Level 5 facilities converted to the ATC system, while controllers at Level 1 facilities continued to be paid under the GS system. When the appellants eventually transferred from Level 1 facilities to higher level facilities in late 1999, the FAA determined their ATC level and pay band by applying the conversion formula to the GS level and step they held while working at the Level 1 towers.
The source of the appellants’ complaint is that air traffic controllers who transferred to higher level towers prior to October 1998 were promoted to higher pay grades to correspond to the higher level of their new jobs within the GS system. Those air traffic controllers transferred within the GS system; because their transfer to a higher level facility was accompanied by a grade increase under the GS system, they were entitled under 5 U.S.C. § 5334(b) to be paid at a step level within the higher grade that was two steps above the level at which they were being paid in the lower rated facility. Because the appellants transferred from the Level 1 facilities after October 1998, they transferred from the GS system directly into the ATC pay system. They therefore did not receive the benefit of the statutory two-step increase that they would have received if they had been transferred at a time when the GS system was still in effect for the facilities to which they transferred. As a result, the appellants were assigned a lower ATC level and pay band than similarly situated controllers who transferred from Level 1 facilities before the ATC system took effect. The appellants allege that the FAA’s failure to promote them within the GS system before converting them to the ATC system caused them to lose the two-step increase guaranteed by section 5334(b).
II
The appellants contend that, upon their transfer to the higher level towers, they were entitled to a pay increase under section 5334(b). That statute provides in relevant part as follows:
An employee who is promoted or transferred to a position in a higher grade is entitled to basic pay at the lowest rate of the higher grade which exceeds his existing rate of basic pay by not less than *1374two step-increases of the grade from which he is promoted or transferred.
5 U.S.C. § 5334(b). The effect of section 5334(b) is to ensure that all employees who are promoted to a higher GS grade receive an increase in pay, not a reduction. Because the pay associated with high steps in one grade is often greater than the pay associated with low steps in the next higher grade, a promotion from, for example, GS-10, step 10, to GS-11, step 1, would entail a loss of pay if it were not for the operation of section 5334(b).
While section 5334(b) ensures that grade promotions within the GS system do not result in a loss of pay, the case law makes clear that section 5334(b) applies only to employees who transfer from one position in the GS system to another position that is also within the GS system. See United States v. Clark, 454 U.S. 555, 561, 102 S.Ct. 805, 70 L.Ed.2d 768 (1982) (holding that section 5334(b) does not apply to a transfer from a non-GS system position into a GS system position); Libretto v. United States, 230 Ct.Cl. 790, 791 (1982) (holding that section 5334(b) does not apply to a transfer from a GS system position into a non-GS system position). The question presented by this case is whether the appellants’ transfers from Level 1 towers to higher level facilities were transfers within the GS system or transfers from the GS system into a non-GS system.
The appellants rest their claim on the theory that each of their transfers consisted of two steps: first, a promotion from a Level 1 facility to a higher level facility within the GS system (thus triggering section 5334(b)); and second, a conversion from the GS system into the ATC system by operation of Rule 35 of the collective bargaining agreement. Although the appellants characterize the two-step conversion process as a question of fact, they point to no factual evidence in dispute. Indeed, the existence of a first GS-to-GS step is contradicted by the allegations in the appellants’ own complaint. As they assert repeatedly, by the time they transferred to higher level facilities, those facilities had already transitioned to the ATC system. Thus, at the time they actually received their promotions, their new positions fell outside the GS system. All of the appellants’ arguments to the contrary are conclusory; they offer no proof beyond the fact that air traffic controller positions at those facilities had previously been classified within the GS system. As the complaint acknowledges, air traffic controller positions at Level 2 through Level 5 facilities were within the GS system prior to October 1998 and within the ATC system thereafter. At the time the appellants moved to higher level facilities in 1999, they were moving from GS positions to non-GS positions. Under those circumstances, section 5334(b) is inapplicable.
While it may be that the parties to the collective bargaining agreement should have anticipated that some controllers would lose the benefit of section 5334(b) if they did not transfer into a higher level facility until after the conversion to the ATC pay system, the agreement did not provide a remedy for those employees, and federal law does not provide a remedy, either. It may be that the collective bargaining process can rectify the problem, at least for the future. But what is clear from the collective bargaining agreement and section 5334(b) is that when the appellants transferred to their new facilities, they transferred out of the GS pay system and into the ATC pay system; they never transferred to a higher grade within the GS system and thus were not entitled to *1375the benefits of the two-step increase in pay received by controllers who transferred at a time when the GS system was in effect for all the facilities.
Although our legal analysis of the plaintiffs’ claim under section 5334(b) tracks that of the Court of Federal Claims, that court dismissed the case for lack of jurisdiction and not on the merits. In that respect, we disagree with the court’s disposition. The trial court agreed that section 5334(b) is a “money-mandating statute” and that if the appellants had been able to show they were persons entitled to the benefits of that statute, they would have been entitled to relief from the Court of Federal Claims. Where plaintiffs have invoked a money-mandating statute and have made a non-frivolous assertion that they are entitled to relief under the statute, we have held that the Court of Federal Claims has subject-matter jurisdiction over the case. See Fisher v. United States, 402 F.3d 1167, 1175-76 (Fed.Cir.2005); see also Doe v. United States, 463 F.3d 1314, 1323-26 (Fed.Cir.2006); In re United States, 463 F.3d 1328, 1335 (Fed.Cir.2006).
An unusual quirk in this case is that at the time of their transfer from the Level 1 facilities, the plaintiffs were not technically being paid pursuant to the GS schedule set forth in title 5 of the U.S. Code, but instead were being paid pursuant to the FAA’s Personnel Management System, the administrative order that adopted the GS pay system for the interim period pending conversion of the air traffic controllers to the ATC system. The statute that authorized the Administrator to implement a compensation scheme for the agency in 1996 also provided that the portions of title 5 containing the GS system would no longer apply to FAA employees. See 49 U.S.C. § 40122. After April 1, 1996, FAA employees such as the plaintiffs were therefore being paid in accordance with the GS compensation system, but because of administrative order, not because of statutory direction.
That unusual feature does not alter our analysis of the jurisdictional issue, however, because the Court of Federal Claims has jurisdiction over money claims founded not only on statutes, but also on “any regulation of an executive department.” 28 U.S.C. § 1491. An agency directive dealing with personnel policy qualifies as such a regulation if (1) the agency was authorized to issue the regulation; (2) the agency conformed to all procedural requirements in promulgating the regulation; (3) the agency intended the regulation to create a binding rule; and (4) the provision does not contravene a statute. Hamlet v. United States, 63 F.3d 1097, 1105 (Fed.Cir.1995).
The FAA’s adoption of the GS pay system in the 1996 Personnel Management System clearly qualifies as a regulation under that test. It was specifically authorized by statute and is not in conflict with the GS system compensation provisions or any other law; it was promulgated by the Administrator as directed by Congress; as a regulation dealing with “a matter relating to agency management or personnel,” formal rulemaking was not required, 5 U.S.C. § 553(a)(2); and the agency’s statement, in mandatory language, of its intention to continue to pay employees under the GS scale plainly reflects an intention to be bound by the compensation policy set forth in the regulation. See Hamlet, 63 F.3d at 1105-06 & n. 6. Treating the references to section 5334(b) in the complaint as directed to the Administrator’s regulatory *1376adoption of the standards of that statute as well as the other portions of the GS statutory scheme, we hold that the Personnel Management System was a binding, money-mandating regulation and that the Court of Federal Claims had jurisdiction over the plaintiffs’ claim on that basis. The dismissal in this case therefore should have been for failure to state a claim upon which relief can be granted, not for lack of jurisdiction. Because the distinction between the two forms of dismissal has no apparent practical effect in this case, however, we need not remand for purposes of correcting the judgment in that respect. See Lewis v. United States, 70 F.3d 597, 603-04 (Fed.Cir.1995); see also Doe v. United States, 463 F.3d at 1325 (dismissal of claim for want of jurisdiction was error, but error was harmless because action should have been dismissed on the merits); Moden v. United States, 404 F.3d 1335, 1340-41 (Fed.Cir.2005) (same). Instead, we merely note that for any possible future effect that the judgment in this case may have, the dismissal should be regarded as a dismissal on the merits rather than for want of jurisdiction.
Each party shall bear its own costs for this appeal.
AFFIRMED.
. The GS system is the compensation scheme commonly used for employees of the federal government in administrative, professional, and technical positions. In 1995 and 1996, Congress enacted legislation authorizing the FAA Administrator to implement a new personnel management system for FAA employees, including fixing the compensation and benefits of employees and officers. See Pub. L. No. 104-50, § 347, 109 Stat. 460 (1995); 49 U.S.C. §§ 106(1)> 40122(a). Pursuant to that authorization, the Administrator promulgated the FAA Personnel Management System, which kept the GS compensation system in effect for an interim period beginning on April 1, 1996, until the new pay system could be developed and fully implemented.