E. GRADY JOLLY, Circuit Judge:

The sole issue we decide on this appeal is when the statute of limitations began to run on Barrett's claim against the union that it allegedly breached its duty to him of fair representation.

Barrett was employed by Ebasco at the South Texas Nuclear Project and was represented by the United Brotherhood of Carpenters and Joiners of America, Local 1084. *171 He was fired on November 9, 1984, for use and possession of marijuana. The union filed a grievance protesting Barrett’s discharge, which it processed through all appropriate steps of the grievance procedure under the collective bargaining agreement. When Ebasco finally denied the grievance, the union continued to press Barrett’s case by demanding arbitration. The union represented Barrett throughout the arbitration proceeding, including posthearing submissions. The arbitrator denied the grievance and sustained the discharge. Barrett received a copy of the arbitration award on or about November 18, 1985. Although Barrett filed a lawsuit against Ebasco in January 1986, which sought to set aside and vacate the arbitration award, it was not until October 1986 that Barrett filed an amended complaint, naming the union as an additional party (after it had voided his membership in June 1986), and alleging for the first time a claim that the union breached its duty of fair representation under 29 U.S.C. § 185(a).

In January 1988, the district court granted summary judgment in favor of Ebasco and the union and dismissed the complaint. Although the district court decided the case on alternative grounds, we need only address the statute of limitations question.

It is uncontested that the statute of limitations period applicable to this case is six months. DelCostello v. Teamsters, 462 U.S. 151, 169, 103 S.Ct. 2281, 2293, 76 L.Ed.2d 476 (1983). The statutory period begins to run when the plaintiff either knew or should have known of the injury itself, i.e., the breach of duty of fair representation, rather than of its manifestations. Farr v. H.K. Porter Co., 727 F.2d 502, 505 (5th Cir.1984). The only breaches of duty of fair representation by the union that Barrett alleges in his amended complaint occurred during the arbitration hearing in March 1985. Since, according to his own allegations, the union’s only breach of its duty to represent him fairly occurred at the arbitration hearing, it is clear to us that the six-month limitations period began to run once these alleged breaches were known or should have been known to him. We need not decide whether these breaches were known to him at the time of the hearing, or when he received the arbitrator’s report denying his grievance and sustaining the discharge; in either event, the six-months period had long-since passed when he filed his amended complaint that first named the union as a party and raised for the first time a breach of the duty of fair representation.

Barrett misses the point when he argues that from the date of the arbitrator’s decision until the union voided his membership in June 1986, he had no knowledge of the defendant union’s “sudden opposition” to his position. The question is not when the union abandoned its support of Barrett, but when the union breached its duty of fair representation. The union did not represent Barrett at any point during his litigation in court, nor was it obligated to do so. The scope of the duty of fair representation is coextensive only with the union’s statutory authority to act as the exclusive representative of all employees within the bargaining unit. If a union does not serve as the exclusive agent for the members of the bargaining unit with respect to a particular matter, there is no corresponding duty of fair representation. Price v. International Union, United Automobile Aerospace and Agricultural & Implement Workers of America, Local 571, 795 F.2d 1128, 1134 (2d Cir.1986), cert. denied, 487 U.S. -, 108 S.Ct. 2890, 101 L.Ed.2d 924 (1988); Freeman v. Local Union No. 135, 746 F.2d 1316, 1321 (7th Cir.1984); Dycus v. NLRB, 615 F.2d 820, 827 (9th Cir.1980). In this case, the union did not have the exclusive right to seek judicial review of the arbitrator’s award, as it did under the collective bargaining agreement to determine whether his case should be grieved and arbitrated. Indeed, Barrett exercised his own individual remedies outside the collective bargaining agreement when he filed this suit. As the Seventh Circuit noted in Freeman:

Once the arbitrator denied plaintiff’s grievance, the rationale for the duty of fair representation evaporated; Freeman no longer needed the protections provid *172 ed by the duty of fair representation because he had access to extra-contractual remedies. That being the case, the union owed plaintiff no duty in deciding whether to seek judicial review of the committee’s ruling because, with respect to that decision, it was not acting as his exclusive representative. The union was under no duty to provide Freeman with more legal assistance than bargained for in the contract or required by law.

Freeman, 746 F.2d at 1321-22.

Finally, since it is an “indispensable predicate” to a section 301 action against the employer to establish that the union has breached its duty of fair representation, Holmes v. Greyhound Lines, Inc., 757 F.2d 1563, 1567 (5th Cir.1985), it follows that the district court correctly dismissed the complaint against Ebasco, as well. As we said in Holmes: “Because his claims against the Union are indisputably time-barred, the district court would not be authorized to reach the merits of [the plaintiffs] claims against [the defendant employer].” 757 F.2d at 1567.

The judgment of the district court is therefore

AFFIRMED.