
648 P.2d 788 (1982)
98 N.M. 330
Pauline CHRISTMAS, Plaintiff-Appellee,
v.
CIMARRON REALTY COMPANY and Bill Littrell, Defendants-Appellants.
No. 13694.
Supreme Court of New Mexico.
June 30, 1982.
Rehearing Denied July 19, 1982.
*789 John W. Danfelser, Albuquerque, for defendants-appellants.
Paul A. Kastler, Raton, for plaintiff-appellee.
Sommer & Lawler, Joseph G. Lawler, Houston Lee Morrow, Santa Fe, amicus curiae.

OPINION
RIORDAN, Justice.
Plaintiff, Pauline Christmas (Christmas), brought an action against defendants, Cimarron Realty (Cimarron) and its sole owner, Bill Littrell (Littrell), for breach of contract. The complaint alleged that Christmas, a licensed real estate agent, and a former employee of Littrell, was owed a commission on a piece of property sold by Littrell, a licensed real estate broker.
Littrell moved to compel arbitration of the dispute pursuant to the Uniform Arbitration Act. §§ 44-7-1 through 44-7-22, N.M.S.A. 1978. Littrell claims that under Article 14 of the National Association of Realtors, Code of Ethics (1974), the parties are required to submit the dispute to arbitration. The trial court denied Littrell's motion to compel arbitration. We affirm.
The issue on appeal is whether arbitration is required under the National Association of Realtors Code of Ethics when the realtors were both members of the same firm at the time the contract was entered into but were later associated with different firms when the action was brought. Most of the facts on appeal are not in dispute. We do not resolve the question of whether Christmas is entitled to a commission. We only decide the issue of arbitration.
In early 1978, Christmas was employed by Littrell and his partner as a salesperson in their office of Cimarron Realty Co. Pursuant to the agency employment contract, Christmas was to receive a minimum of 40% of all real estate brokerage fees paid to the company as a result of sales of listings she had obtained. During her employment with Littrell and his partner, Christmas obtained a listing for the Burner Ranch.
In July 1978, the partnership terminated; and Christmas went to work for a different firm. After obtaining a broker's license, Littrell resumed listing and selling realty as a sole proprietorship under the name "Cimarron Realty". He later sold the Burner *790 Ranch, apparently under the same listing that Christmas had obtained. Cimarron received a commission of $100,000.00. Christmas claims she is entitled to $40,000.00 of the commission. At the time the ranch was sold and the brokerage fee was earned, the parties were not associated with the same real estate firm.
During all pertinent times, Christmas and Littrell were both realtors subject to Article 14 of the Realtors' Code of Ethics by virtue of membership in their local boards of realtors and the state and National Association of Realtors. Article 14 states:
In the event of a controversy between Realtors associated with different firms, arising out of their relationship as Realtors, the Realtors shall submit the dispute to arbitration in accordance with the regulations of their board or boards rather than litigate the matter. [Emphasis added.]
Arbitration is a contractual remedy for the settlement of disputes by extra-judicial means. King County v. Boeing Co., 18 Wash. App. 595, 570 P.2d 713 (1977). Parties contracting to resolve disputes by arbitration are bound by their agreement. Loukonen v. MacKay, 490 P.2d 78 (Colo. App. 1971). The terms of the agreement define the scope of the jurisdiction, conditions, limitations and restrictions on the matters to be arbitrated. See International Service Insurance Company v. Ross, 169 Colo. 451, 457 P.2d 917 (1969).
The terms of the arbitration agreement are to be interpreted by the rules of contract law. See Gonzales v. United Southwest Nat. Bank, 93 N.M. 522, 602 P.2d 619 (1979). It is a well established principle of contract law that courts will not rewrite a contract for the parties. Brown v. American Bank of Commerce, 79 N.M. 222, 441 P.2d 751 (1968). It is also established that courts will apply the plain meaning of the contract language as written in interpreting terms of a contract. Clear v. Patterson, 80 N.M. 654, 459 P.2d 358 (1969); Estrada v. Planet Insurance Company, 26 Ariz. App. 103, 546 P.2d 372 (1976); Fuller & Co. v. Mountain States Investment Builders, 37 Colo. App. 201, 546 P.2d 977 (1975), cert. denied (Feb. 23, 1976). Therefore, the literal reading of this provision must be given effect.
As we read Article 14, the "plain meaning" of the provision requiring arbitration limits its scope to controversies arising from relationships between realtors from different firms. We view the dispute brought before the lower court as one that arose from a contractual relationship between the parties when they were members of the same firm. If we were to compel Christmas to arbitrate her dispute with Littrell, we would be inserting a new clause into an otherwise unambiguous contract.
As stated by the Illinois Supreme Court:
[P]arties are only bound to arbitrate those issues which by clear language they have agreed to arbitrate; arbitration agreements will not be extended by construction or implication.
Flood v. Country Mutual Insurance Company, 41 Ill.2d 91, 94, 242 N.E.2d 149, 151 (1968).
The order of the district court denying the motion to compel arbitration is affirmed. The matter is remanded to the district court for trial.
IT IS SO ORDERED.
EASLEY, C. J., and PAYNE, J., concur.
