
833 F.Supp. 420 (1993)
NATIONAL CLEANING CONTRACTORS, INC., Plaintiff,
v.
LOCAL 32B-32J, SERVICE EMPLOYEES INTERNATIONAL UNION, Realty Advisory Board on Labor Relations Inc., and Cohen Brothers Realty Co., Defendants.
No. 92 Civ. 7875 (PNL).
United States District Court, S.D. New York.
October 15, 1993.
*421 Kauff, McClain & McGuire, New York City (Kevin G. Chapman, of counsel), for plaintiff.
Manning, Raab, Dealy & Sturm, New York City (Paul Galligan, of counsel), for defendant Local 32B-32J, Service Employees Intern. Union.
Steven M. Coren, New York City (Steven M. Coren, Randy L. Braun, of counsel), for defendant Cohen Bros. Realty Co.

OPINION AND ORDER
LEVAL, District Judge.
The motions before the court relate to the arbitration of a grievance filed over the discharge of one Roy McKenzie, an office maintenance worker. The arbitrator's Opinion and Award found that defendant Cohen Brothers, managers of an office building where McKenzie worked at the time of discharge, violated its collective bargaining agreement with McKenzie's union by improperly discharging him. The arbitrator found that National Cleaning Contractors, which previously had been McKenzie's employer, did not transfer McKenzie or otherwise violate its agreement with McKenzie's union. However, the arbitrator found that National Cleaning bore some of the responsibility for Cohen Brothers' wrongful discharge. The arbitrator's award ordered that Cohen Brothers pay 85% of McKenzie's back wages; that National pay 15% of McKenzie's back wages, and that National reinstate McKenzie.
Defendant Cohen Brothers moves to vacate the arbitration award. Plaintiff National Cleaning cross-moves for summary judgment modifying or vacating the award. Defendant union Local 32B-32J cross-moves to confirm the arbitration award.

Background
In the first part of 1992, National provided contractual cleaning services at 805 Third Avenue; McKenzie was a National employee assigned to that site. The parties to the cleaning contract agreed to terminate it as of May 31, 1993 and Cohen Brothers, Managing Agent of 805 Third Avenue, assumed responsibility for cleaning as of that date.
Two days before the termination of the National Cleaning contract, the building manager, an employee of Cohen Brothers, asked National to transfer McKenzie from the site for alleged wrongdoing. National sent a replacement for McKenzie over the next few days, which the manager took to mean that his transfer request had been granted. However, McKenzie was in fact out sick those days. When McKenzie returned to work June 3, Cohen Brothers asserted he was an employee of National, and National insisted he was an employee of Cohen Brothers. Neither gave him employment.
One question at issue in the arbitration was whether National transferred McKenzie from 805 Third Avenue to other employment at National on May 29. This was important for several reasons. The collective bargaining agreement that the Union asserts it had with Cohen Brothers provided that, when a cleaning function was passed from one covered contractor to another, the workers at *422 the site would become the employees of the successor contractor. Accordingly, if McKenzie was employed by National at the 805 Third Avenue site on June 1, he became Cohen's employee and Cohen violated its collective bargaining agreement (assuming the agreement alleged was in force) by failing to accept McKenzie as an employee on that date. On the other hand, if McKenzie was transferred from 805 Third Avenue, National violated its collective bargaining agreement by summarily transferring him.
The collective bargaining agreement that allegedly binds Cohen Brothers is between the Realty Advisory Board on Labor Relations (RAB) and the Union. RAB is a multi-employer organization authorized by its members to enter into a collective bargaining agreement for the employers' workers who are represented by the Union. The Union and National assert that Cohen Brothers is a member of RAB and thus bound by its contract with the Union; Cohen Brothers denies membership in RAB. National is a member of a different multi-employer group, Service Employers Association (SEA). SEA members are all building services contractors. SEA, like RAB, is authorized by its member employers to enter into a collective bargaining agreement with the Union, which represents the employers' workers. It is undisputed that National is bound by SEA's contract with the Union.
After McKenzie's discharge, the Union sent a notice of intent to arbitrate to both National Cleaning and Cohen Brothers on June 24, 1991.[1] The SEA contract and the RAB contract each provided for arbitration of such disputes.
The arbitrator resolved these disputes as follows: The arbitrator found that National had not transferred McKenzie to other employment on May 29. Thus on June 1, when Cohen Brothers took over National's cleaning work at 805 Third Avenue, McKenzie was still employed at 805 Third Avenue and became Cohen Brothers' employee. National was thus found not to have breached the collective bargaining contract. Cohen Brothers, on the other hand, was found to have breached its contract by refusing to honor McKenzie's employment. Cohen Brothers was thus liable for back pay. However, the arbitrator assessed some liability against National for its failure to make clear to Cohen Brothers its refusal to transfer McKenzie. On that basis, the arbitrator ordered National to pay 15% of McKenzie's back pay. Further, the arbitrator declined to order Cohen Brothers to reinstate McKenzie because Cohen Brothers "entertained suspicions about McKenzie's integrity," and ordered National to hire McKenzie in a position comparable to that he had lost at 805 Third Avenue.

Discussion

National Cleaning's motion for summary judgment.
National moves under 9 U.S.C. §§ 10-11 to vacate or modify the award. National advances its motion on two grounds: (1) the arbitrator had no jurisdiction to impose a remedy against National after he found that National did not violate its collective bargaining agreement; and (2) the arbitrator's award was based on authority derived from the collective bargaining agreement between the Union and RAB, and National was neither a signatory to that agreement nor did National otherwise agree to arbitration.
National acknowledges that it is a signatory to the SEA agreement, which requires arbitration for labor disputes, but nonetheless contests the arbitrator's jurisdiction over it in the McKenzie matter. I reject National's argument. National was a party to the SEA agreement with the Union. The Union's charge that National improperly discharged McKenzie in violation of that agreement was arbitrable. Accordingly there is no substance to National's contention that it should not have been subjected to arbitration.[2]
*423 National's other argument is that the arbitrator's award against it was an exercise of his power under the RAB agreement, and because that agreement does not bind National, it cannot be the basis for an award against National. National reasons that even if the arbitration was properly brought under both the SEA agreement (which bound National) and the RAB agreement (which allegedly bound Cohen Brothers), the arbitrator's power under the SEA agreementand thus, his power to issue an award against National essentially ceased with his finding that National did not violate the SEA agreement.
The SEA agreement specifically empowers the arbitrator "to grant any remedy required to correct a violation of this Agreement." (SEA Agmt., Art. VII, ¶¶ 1, 4.) The arbitrator found that National did not violate the SEA agreement by agreeing to transfer McKenzie from 805 Third Avenue. (Arb. Op. & Award at 6.) The arbitrator nonetheless made an award against National on the ground that because "National, by its supervisor, conveyed, as he should not have, that the request [to transfer McKenzie] might even be entertained," National was partially responsible for Cohen Brothers' "erroneous assumption" that McKenzie had been transferred and McKenzie's subsequent loss of his job.
I find, for the reasons that follow, that the arbitrator exceeded his powers when he made an award against National despite his finding that National had not violated its agreement with the Union, and grant National's motion to modify the award by vacating the remedies against National.
Judicial review of an arbitrator's award has a very narrow scope. "[A]s long as the arbitrator is even arguably construing or applying the contract and acting within the scope of his authority," United Paperworkers Int'l Union v. Misco, Inc., 484 U.S. 29, 38, 108 S.Ct. 364, 371, 98 L.Ed.2d 286 (1987); Leed Architectural Products, Inc. v. United Steelworkers Local 6674, 916 F.2d 63, 65 (2d Cir.1990), the arbitrator's decision must be allowed to stand. See 9 U.S.C. §§ 10-11 (specifying narrow grounds for modification or vacatur of arbitration award). However, as National points out, the deference due to arbitrators' awards does not grant them limitless power. "[A]n arbitrator is confined to interpretation and application of the collective bargaining agreement; he does not sit to dispense his own brand of industrial justice." United Steelworkers v. Enterprise Wheel & Car Corp., 363 U.S. 593, 597, 80 S.Ct. 1358, 1361, 4 L.Ed.2d 1424 (1960); Leed, 916 F.2d at 65. National submits, and I agree, that the arbitrator exceeded his powers when he allocated part of Cohen's liability and Cohen's reinstatement obligation to National.
The arbitrator found that Cohen Brothers violated its collective bargaining agreement, and that Cohen Brothers was liable for that violation. The arbitrator found that National did not violate the agreement. But, because he found that Cohen's violation was caused in part by National's misleading indication that McKenzie might be transferred, he imposed a portion of Cohen's liability on National. The arbitrator had no power to impose any part of Cohen Brothers' liability on National.
Because National's collective bargaining contract with the Union included an arbitration clause, the arbitrator had the power to make an award against National for any breach by National of its contract. Because Cohen Brothers' collective bargaining contract contained an arbitration clause, the arbitrator had the power to make an award against Cohen Brothers for any breach by Cohen Brothers of its contract. There was, however, no arbitration agreement between Cohen Brothers and National. If National in some way violated Cohen Brothers' rights, entitling Cohen Brothers to contribution, indemnity, or damages, for any liability incurred by Cohen Brothers, Cohen Brothers needed to sue National in a court of law to enforce such a claim. The mere happenstance that the arbitrator entertained the parallel arbitrable claims of the Union against National and against Cohen Brothers did not give the arbitrator any power to adjudicate rights as between National and Cohen Brothers. Because Cohen Brothers was found to have breached its labor contract, the arbitrator could properly award *424 remedies against Cohen Brothers. Because National was found not to have breached the arbitrable labor contract, the arbitrator could not award remedies against National. The arbitrator had no power to transfer any part of Cohen Brothers' responsibility onto National.
9 U.S.C. § 11(b) provides for judicial modification of an arbitrator's award "Where the arbitrators have awarded upon a matter not submitted to them...." The arbitrator's determination of National's contribution to Cohen Brothers' violation of the agreement was a "matter not submitted" to him. This court thus has clear authority to modify the award to the extent that it imposes liability on National.
National Cleaning's motion to modify the award by striking those portions that impose liability and obligations on National is granted, without prejudice to any action for contribution that Cohen Brothers may wish to institute in the proper forum.

Cross motions by Cohen Brothers and Union to vacate and affirm the award.
Cohen Brothers moves under 9 U.S.C. § 10(a)(4) to vacate the award, or alternatively under 9 U.S.C. § 11 to modify the award, on the ground that it did not agree to arbitration, is not a member of RAB, did not participate in the arbitration and did not employ McKenzie.
Party consent is the cornerstone of arbitration. "[A]rbitration is a matter of contract and a party cannot be required to submit to arbitration any dispute which he has not agreed so to submit." United Steelworkers v. Warrior & Gulf Navigation Co., 363 U.S. 574, 582, 80 S.Ct. 1347, 1353, 4 L.Ed.2d 1409 (1960); Litton Financial Printing Div. v. NLRB, ___ U.S. ___, ___, 111 S.Ct. 2215, 2222, 115 L.Ed.2d 177 (1991). If Cohen Brothers did not consent to arbitration, the award against it cannot stand.
Cohen Brothers' consent to this arbitration is derived from its alleged membership in RAB, whose contract with the Union binds its member employers to arbitrate grievances. Cohen Brothers asserts that it is not a member of RAB and thus was not bound by this agreement to arbitrate. As evidence, it offers the affidavit of its president, Charles Cohen, to the effect that it has never been a member of RAB, and that it did not participate in the arbitration hearing as a party. (Cohen Aff. ¶¶ 3-4.) To support its contention that Cohen Brothers is a member of RAB, the Union submits purported RAB membership lists (Galligan Aff. at ¶ 5 and Union Exs. B and C). Cohen Brothers in turn challenges whether these are in fact RAB membership lists.
The record presents conflicting evidence on whether Cohen Brothers was a signatory to the RAB agreement. This issue may be dispositive to the motion by Cohen Brothers to vacate or modify the award, and requires an evidentiary hearing for its resolution.[3] Nor can the Union's motion to affirm the award be decided before a hearing to resolve this issue.

Conclusion
National Cleaning's motion for summary judgment modifying the award to eliminate the finding of liability and award against it is granted. The Union's motion to affirm the award is denied. Cohen Brothers' motion to vacate the award requires a hearing, which is scheduled for November 12, 1993, at 10:00 a.m., on the issue of whether Cohen Brothers is a signatory to the collective bargaining agreement between the Realty Advisory *425 Board on Labor Relations (RAB) and the Union.
SO ORDERED.
NOTES
[1]  The June 24 notice of intent to arbitrate requested that McKenzie's discharge be added to two pending requests to arbitrate other complaints by McKenzie against National Cleaning. The June 24 notice also added Cohen Brothers as an employer.
[2]  The arbitration clause provides that there shall be a Contract Arbitrator empowered to decide all issues pertaining to interpretation, application and performance of the contract and "to grant any remedy required to correct a violation of this Agreement." (SEA Agmt., Art. VII, ¶¶ 1, 4, appearing at National Ex. B.)
[3]  The Union also argues that Cohen Brothers waived any objection to the arbitrator's jurisdiction by participating in the arbitration, and by failing to raise this objection earlier. It supports its contention that Cohen Brothers' participated in the arbitration as a party with hearing notices naming Cohen Brothers as a party, and sign-in sheets showing that officers of Cohen Brothers attended the arbitration hearings (Union Exs. H and I). Cohen Brothers responds by affidavit that "Cohen Brothers Realty routinely advised the arbitrator that it was not a party to the arbitration." (Cohen Aff. Feb. 11, 1993 at ¶ 6) Although the affiant does not purport to have communicated with the arbitrator himself on this subject, I do not reach the issue of waiver because the record at this time does not permit me to find that Cohen Brothers willingly participated in the hearing.
