SUMMARY ORDER
Plaintiff-appellant Patrick Ellis appeals an award of summary judgment in favor of Secretary of Labor Elaine L. Chao on Ellis’s challenge to the Secretary’s decision not to sue to set aside the results of a Civil Service Employees Association election pursuant to Section 402 of the Labor-Management Reporting and Disclosure Act of 1959 (“LMRDA.”).1 See Ellis v. Chao, 329 F.Supp.2d 454 (S.D.N.Y.2004); 29 U.S.C. § 482. The case has previously been before us, see Ellis v. Chao, 336 F.3d 114 (2d Cir.2003), and we assume the parties’ familiarity with the facts and record of prior proceedings, which we reference only as necessary to explain our decision.
We review the district court’s grant of summary judgment de novo, and we will affirm only if the record, viewed in the light most favorable to Ellis, reveals no genuine issue as to any material fact and the Secretary is entitlement to judgment as a matter of law. Fed.R.Civ.P. 56(c); Hughes v. Bricklayers & Allied Craftworkers Local 45, 386 F.3d 101 (2d Cir.2005).
In considering a challenge to the Secretary’s decision not to institute suit to set aside a union election, we are “not authorized to substitute [our] judgment for the decision of the Secretary.” Dunlop v. Bachowski, 421 U.S. 560, 571, 95 S.Ct. 1851, 44 L.Ed.2d 377 (1975), abrogated on other grounds, Local No. 82, Furniture & Piano Moving v. Crowley, 467 U.S. 526, 550 n. 22, 104 S.Ct. 2557, 81 L.Ed.2d 457 (1984). Except in “rare” cases — as when the Sec*20retary abrogates her LMRDA enforcement responsibility, prosecutes complaints in a constitutionally discriminatory manner, or otherwise clearly defies the LMRDA, id. at 574, 95 S.Ct. 1851 — our review is “confined to examination of the ‘reasons’ statement” supporting the Secretary’s decision to determine if that decision is so irrational as to be “arbitrary and capricious,” id. at 572-73, 95 S.Ct. 1851; Ellis v. Chao, 336 F.3d at 122-25. On this appeal, Ellis contends that the Secretary’s Supplemental Statement of Reasons, issued in response to our earlier ruling in this case, id. at 127, demonstrates both her clear defiance of the LMRDA and the arbitrary and capricious nature of her decision. We conclude that plaintiffs argument is without merit.
Preliminarily, we observe that the Supplemental Statement identifies and applies the correct legal standard and also remedies the particular defects identified by this court in the original Statement of Reasons so as to permit meaningful judicial review of the Secretary’s challenged decision. Id. at 122-25; see also Dunlop v. Bachowski, 421 U.S. at 573, 95 S.Ct. 1851 (noting that “a statement of reasons must be adequate to enable the court to determine whether the Secretary’s decision was reached for an impermissible reason or for no reason at all”). It provides, inter alia, a detañed account of the process by which the Secretary conducted her investigation, the findings made in the course thereof, and the reasoning behind the ultimate conclusion that the identified observation violations nevertheless did not affect the outcome of the election.
To the extent Ellis, and especiaUy the amicus, argue that the Secretary’s finding of observer violations presumptively requires her to sue to challenge the election results, we cannot agree. As we noted when this case was last before us, there is “no support” for the “suggestion that it would never be possible for the Secretary to legitimately reach the conclusion that observer violations occurred but could not have affected the outcome of a given election.” Ellis v. Chao, 336 F.3d at 126. Wirtz v. Hotel, Motel & Club Employees Union, Local 6, 391 U.S. 492, 88 S.Ct. 1743, 20 L.Ed.2d 763 (1968) warrants no different conclusion, because that case focused on LMRDA § 401(e), which affords quite different protections from the observer rights conferred by § 401(c), see id. at 506-07, 88 S.Ct. 1743.
Insofar as Ellis points to various factual circumstances relating to the challenged election to argue that the Secretary’s decision not to sue must be deemed defiant of the law, or at least arbitrary and capricious, we are not convinced. The Supplemental Statement, in contrast to the original Statement of Reasons, makes plain that the Secretary conducted a thorough investigation, and it specifies rational reasons for her conclusion that, despite the problems identified, “there was no violation of section 401 of the LMRDA that may have affected the outcome of the election.” Although Ellis complains that the Secretary failed to conduct an independent tally of the ballots at issue, neither this court’s earlier decision, the LMRDA, nor any other precedent mandates an independent tally to permit the Secretary to reach a rational conclusion or for this court to review that decision.
The observer rights at issue in this case are an important procedure that ensure free and fair union elections, which are themselves critical to protecting and promoting the interests of represented workers. Thus, we do not minimize the significance of the violations identified by the Secretary in her investigation. Nevertheless, because the Secretary has now clarified the processes by which she considered *21the effect of these violations on the election, and because the Secretary’s reasons for concluding that the violations had no effect on the outcome are not irrational, her decision not to file suit to challenge the election cannot be deemed arbitrary and capricious. Under these circumstances, the district court properly granted summary judgment in favor of the Secretary.
The August 10, 2004 judgment of the district court is hereby AFFIRMED.
. Ellis is supported in his appeal by amicus curiae Association for Union Democracy, Inc. We refer simply to "Ellis” in noting the challenges raised by him and the amicus to the summary judgment award.