Opinion for the Court filed by Circuit Judge RANDOLPH.
RANDOLPH, Circuit Judge:A union wishing to become the bargaining representative of newly-federalized airport screeners initiated two proceedings, one administrative, the other judicial. The administrative action sought to have the Federal Labor Relations Authority order *311representation elections. The other action sought a judgment from the district court that the screeners had the right to engage in collective bargaining. The FLRA rejected the union’s petition. The district court dismissed the complaint. The question in this appeal is whether the district court had jurisdiction.
In response to the events of September 11, 2001, Congress enacted the Aviation and Transportation Security Act, Pub.L. No. 107-71,115 Stat. 597 (2001), creating a federal workforce to screen passengers and cargo at commercial airports. Section 111(d) of the Security Act, 115 Stat. 620, codified at 49 U.S.C. § 44985 note, provides that “[njotwithstanding any other provision of law, the Under Secretary of Transportation for Security may employ, appoint, discipline, terminate, and fix the compensation, terms, and conditions of employment of Federal service for [federally employed security screeners].”
Thereafter, the American Federation of Government Employees filed several petitions with the Federal Labor Relations Authority, seeking elections among security screeners at a number of airports and certification as the screeners’ exclusive representative for collective bargaining. On January 8, 2003, Under Secretary James M. Loy issued a directive stating that, “[b]y virtue of the authority vested in the Under Secretary of Transportation for Security in Section 111(d),” federally employed security screeners “shall not, as a term or condition of their employment, be entitled to engage in collective bargaining or be represented for the purpose of engaging in such bargaining by any representative or organization.” The next day, the Transportation Security Administration filed its response to the union’s petitions. The Administration’s main contention was that the FLRA could not order representation elections in view of § 111(d) and Loy’s directive.
One day later the union filed a complaint in the district court seeking an injunction and a declaratory judgment on the ground that Loy “did not have the statutory authority to issue the directive” and that the directive was “arbitrary and capricious agency action in violation of the Administrative Procedure Act, 5 U.S.C. § 706.” The union also challenged the directive on constitutional grounds, asserting that it “deprives affected federal employees of their right to free speech and association under the First Amendment and to equal protection under the Fifth Amendment” to the Constitution.
While the case was pending before the district court, the FLRA’s Regional Director ruled that § 111(d) of the Security Act and the Loy directive relieved the Transportation Security Administration of any “duty to bargain over conditions of employment of security screeners.”
The district court later dismissed the union’s statutory claims, holding that the “FLRA has exclusive authority over conducting elections to determine whether a labor union has the support of a majority of employees in an appropriate unit” and that the “petitions for elections and the TSA objection that the Loy Determination deprives FLRA of jurisdiction to conduct any election are ... properly before that agency,” not the court. 281 F.Supp.2d 59, 62 (D.D.C.2003). As to the constitutional claims, the court took note of the union’s failure to raise these before the FLRA. Id. at 64. Finding the claims insubstantial, the court dismissed this portion of the complaint for failure to state a cause of action. Id. at 66.
In the meantime the FLRA affirmed the Regional Director’s decision dismissing the union’s petitions. United States Dep’t of Homeland Security, et al. and AFGE, AFL-CIO, 59 F.L.R.A. No. 63, 2003 WL 22669101 (Nov. 4, 2003). The FLRA *312agreed that § 111(d) granted “unfettered discretion to the [Under Secretary] to determine the terms and conditions of employment for [federal] screener personnel,” and that the Loy directive validly barred the screeners from engaging in collective bargaining. Id. at *13. Therefore, the union’s “petitions could not be processed” because the FLRA had no authority to conduct elections. Id. at *7. The FLRA refused to consider the union’s constitutional arguments because these were not properly raised before the Regional Director. Id. at *13. The union did not seek judicial review of the FLRA’s decision.
Title VII of the Civil Service Reform Act, 5 U.S.C. §§ 7101-7134, governs labor relations between federal agencies and their employees. One of the FLRA’s exclusive functions is to conduct “elections to determine whether a labor organization has been selected as an exclusive representative by a majority of the [federal] employees in an appropriate unit,” 5 U.S.C. § 7105(a)(2)(B). A union may file a petition with the FLRA alleging that 30 percent or more of the employees in an appropriate unit want the union to represent them in collective bargaining. 5 U.S.C. § 7111(b)(1)(A). The FLRA “shall investigate” such a petition and, if it finds that “a question of representation exists,” it shall conduct or supervise an election after determining who is eligible to vote. 5 U.S.C. § 7111(b)(1)(A) & (d). Any person aggrieved by a “final order” of the FLRA, other than an order under § 7112 (unit determination) or § 7122 (arbitration award), may seek review in the court of appeals. 5 U.S.C. § 7123(a).
If an FLRA order falls within one of § 7123(a)’s two exceptions to review in the court of appeals, this does not mean the district courts are open. It means that review is precluded in any court. Ass’n of Civilian Technicians v. FLRA, 283 F.3d 339 (D.C.Cir.2002). On the other hand, if an FLRA order is not within either exception and is “final,” it may be reviewed only by a court of appeals. The district courts do not have concurrent jurisdiction over matters within the exclusive purview of the FLRA. Karahalios v. Nat’l Fed’n of Fed. Employees, 489 U.S. 527, 533, 109 S.Ct. 1282, 1286-87,103 L.Ed.2d 539 (1989); see United States v. Fausto, 484 U.S. 439, 445, 108 S.Ct. 668, 672-73, 98 L.Ed.2d 830 (1988).
The union thinks it was entitled to sue in district court because this court could not review the FLRA’s refusal to order representational elections. The FLRA rendered its decision under § 7111. Citing U.S. Dep’t of Justice v. FLRA, 727 F.2d 481 (5th Cir.1984), the union states that FLRA rulings under § 7111 are unreviewable. That reads too much into the opinion. The question before the Fifth Circuit was whether an FLRA order requiring a rerun election pursuant to § 7111 was a “final order” under § 7123(a). The court held no because the FLRA had not finally determined if a particular union would represent the employees. 727 F.2d at 493.
The order here is of a different sort. The FLRA’s decision that the screeners could not engage in collective bargaining, and thus were not entitled to union representation, was final in every sense of the word, as counsel for the union admitted at oral argument. We will have a few more words to say on this subject when we discuss the union’s constitutional claims. As to the union’s statutory claims, it is enough to point out that the district court’s jurisdiction did not turn on the presence or absence of our jurisdiction. We cannot review an FLRA unit determination, see 5 U.S.C. § 7123(a)(2), but that does not mean a district court may. Ass’n of Civilian Technicians, 283 F.3d at 340. What matters is whether the union’s claim - that *313the screeners had the right to engage in collective bargaining - was “arguably” within the FLRA’s authority to decide. See American Foreign Serv. Ass’n v. Baker, 895 F.2d 1460,1462 (D.C.Cir.1990). On that score there is no doubt. The union must have thought as much when it filed its election petitions. Title VII gives the FLRA, and the FLRA alone, the authority to order elections so that federal employees may decide who, if anyone, will become them exclusive bargaining representative. In investigating a § 7111 petition the FLRA necessarily must determine that the employees are entitled to engage in collective bargaining. Sometimes the determination will be made in the context of a unit determination. Employees engaged in “security work which directly affects national security,” for instance, cannot be part of a bargaining unit. 5 U.S.C. § 7112(b)(6). Here the FLRA, acting under § 7111, never reached the unit question. It ruled instead that the Security Act plus the Loy directive foreclosed collective bargaining for all federally-employed airport screeners and thus precluded representation elections. We do not say the FLRA was correct. That issue is not properly before us. We do say the FLRA had the exclusive authority to render judgment on the question, subject to review only in a court of appeals pursuant to § 7123.
Citing Aid Ass’n for Lutherans v. U.S. Postal Service, 321. F.3d 1166 (D.C.Cir. 2003), the union argues that even if a statute precluded judicial review of the legality of the Loy directive, this would not deprive the district court of jurisdiction to decide whether Loy acted ultra vires. The short answer is that no statute precludes judicial review of the union’s claims in this regard. Review may be had, but it must be in the court of appeals and it may occur only after the claim has been presented to and finally decided by the FLRA.
We therefore agree with the district court that it did not have jurisdiction over the union’s complaint. The district court nevertheless went ahead and rejected the union’s constitutional claims that the employees had a First Amendment right to engage in collective bargaining and that the Loy directive violated the equal protection component of the Fifth Amendment’s due process clause. We think the court should also have dismissed these claims for lack of jurisdiction. See Sturm, Ruger & Co. v. Chao, 300 F.3d 867, 877 (D.C.Cir.2002). Parties may not bifurcate their case, pursuing only statutory claims before the FLRA while litigating closely related constitutional claims in the district court. NTEU v. FLRA 986 F.2d 537, 539-40 (D.C.Cir.1993); Steadman v. Governor, U.S. Soldiers’ & Airmen’s Home, 918 F.2d 963, 967 (D.C.Cir.1990). That the union did not present its constitutional claims to the FLRA Regional Director is no reason for allowing it to litigate those claims in the district court. To hold otherwise would be to excuse noncompliance with the requirement that one must exhaust administrative remedies on the basis that the party failed to comply. See Steadman, 918 F.2d at 968.
The cases just cited, and analogous cases concerning constitutional claims raised in administrative proceedings, see Shalala v. Illinois Council on Long Term Care, Inc., 529 U.S. 1, 24, 120 S.Ct. 1084, 1099, 146 L.Ed.2d 1 (2000), and Thunder Basin Coal Co. v. Reich, 510 U.S. 200, 214, 114 S.Ct. 771, 779-80, 127 L.Ed.2d 29 (1994), assume that there can be judicial review of the agency’s decision. Citing Bowen v. Michigan Academy of Family Physicians, 476 U.S. 667, 681 n. 12, 106 S.Ct. 2133, 1241 n. 12, 90 L.Ed.2d 623 (1986), the Court in Thunder Basin dropped a footnote stating that there would be a serious constitutional question “if an agency statute were construed to *314preclude all judicial review of a constitutional claim.” 510 U.S. at 215 n. 20, 114 S.Ct. at 780 n. 20. Avoiding that constitutional question might have been an additional factor in favor of finding the FLRA’s dismissal of the union’s petitions a “final order” within § 7123(a), and thus subject to judicial review in this court if the union had raised its First and Fifth Amendment claims in the agency proceedings. But according to the FLRA, the union’s constitutional claims were not properly before it and the union never sought judicial review. At any rate, to decide that the district court had jurisdiction over the union’s constitutional claims we would - at the least - have to assume that the FLRA’s decision on them would have been unreviewable. That assumption would be unwarranted for the reasons we have given.
The district court’s judgment dismissing the complaint is affirmed on the ground that the court lacked jurisdiction.
So ordered.