
130 S.W.3d 359 (2004)
Lynn Rae Levit GOETZ, Appellant,
v.
Joseph Samuel GOETZ, Appellee.
No. 14-02-01164-CV.
Court of Appeals of Texas, Houston (14th Dist.).
February 26, 2004.
Walter P. Mahoney, Jr., Pasadena, for appellants.
Beverly Lord, Norma Levine Trusch, Randall B. Wilhite and Steve A. Bavousett, Houston, for appellees.
Panel consists of Justices RICHARD H. EDELMAN, FROST, and GUZMAN.

OPINION
RICHARD H. EDELMAN, Justice.
In this divorce case, Lynn Goetz appeals portions of the divorce decree (the "decree") on the grounds that the trial court *360 erred in: (1) securing the award of property to Joseph Goetz with a lien on property awarded to Lynn; and (2) deciding it had the authority to appoint an arbitrator, thereby modifying the terms of the parties' mediated settlement agreement (the "MSA"). We affirm.

Lien
Lynn's first issue argues that the trial court erred in securing the money judgment awarded to Joseph with a lien on property that had previously been partitioned to her by the parties' mediated settlement agreement.[1] The relevant portions of the MSA pertaining to the property division contain the following language:
It is stipulated and agreed that the estate of the parties shall be divided as follows:
[Joseph] shall be awarded the following property, and [Lynn] shall be divested of all right, title, interest, and claim in and to such property:
* * * *
[Lynn] shall be awarded the following property, and [Joseph] is hereby divested of all right, title, interest, and claim in and to such property:....
Despite the repeated use of "shall be" in the property division section of the MSA, Lynn contends that the one instance in which "is hereby" is used above transforms the MSA into a partition of the property that was effective, upon its execution by the parties, to change the character of their property from community to separate without approval by the court,[2] (i.e., as contrasted from an agreement incident to a divorce that would have required a finding by the court of a just and right division of marital property in order to be effective).[3] Therefore, Lynn asserts that the lien subsequently imposed by the divorce decree on her previously partitioned separate property divested her of separate property in violation of the Texas Constitution and the laws of Texas.[4]
The first page of the MSA contains the caption for the divorce action in the trial court, and the opening paragraph states, "we stipulate and agree to the following in settlement of the following contested matters before the court in the above-captioned cause." The second paragraph similarly recognizes, "that the Court shall enter a decree of divorce." In addition to providing a detailed property division, the MSA addresses conservatorship of the children, and leaves several unresolved matters pertaining to both for determination by the court, including periods of possession, child support, and the amount of any money judgment payable by either party to the other.
*361 Moreover, although the term "division" is used throughout the MSA, we are unable to find the word "partition" in it.[5] Rather, the decree states that it contains a partition of the community property of the parties and that it shall serve as a muniment of title to transfer ownership of all property awarded to any party therein. The decree also treats the MSA as being incident to the divorce by expressly incorporating it into the decree, acknowledging that the award of property to each party in the decree is in accordance with the MSA, and stating that the trial court found the division of property to be a just and right division of the parties' marital estate. These provisions reflect a clear intent by the parties and the trial court that the MSA was an agreement incident to divorce, rather than a partition agreement. To hold otherwise would render the property division set forth in the divorce decree a nullity because the parties' marital property would have already been partitioned in the MSA and nothing would have remained for division in the decree. Therefore, despite the "is hereby" language used in the MSA, we find no authority or rationale to conclude that such an isolated phrase can overcome the obvious intent of the MSA and decree. Accordingly, Lynn's first issue is overruled.

Authority to Appoint Arbitrator
Lynn's second issue contends that the trial court erred in determining, after the parties were unable to decide on an arbitrator to designate in the MSA, that the trial court had the authority to name one for them if an arbitrable dispute arose and they still could not agree on an arbitrator. In this regard, the relevant portion of the MSA states, in part:
It is further stipulated and agreed that, in the event of disputes regarding periods of possession, extracurricular activities, or rights and duties of the conservators, the parties shall submit the dispute for arbitration with ___. The arbitrator's decision shall be binding on the parties.
(emphasis added). By contrast, the corresponding language of the decree states:
IT IS FURTHER ORDERED AND DECREED that, in the event of disputes regarding periods of possession, extracurricular activities, or rights and duties of the conservators, the parties shall submit the dispute for arbitration with a mutually acceptable arbitrator. If the parties are unable to agree to a mutually acceptable arbitrator, the Court will appoint an arbitrator upon application of a party.

(emphasis added). On the one hand, Lynn argues that she "is not seeking to remove or modify the existing agreement to submit issues to binding arbitration" (emphasis added). On the other hand, however, she asserts that this "agreement" is "contingent on the parties agreeing on the ... person designated or there is no agreement to submit disputed issues to binding arbitration" (emphasis added). Therefore, Lynn contends that the trial court abused its discretion by adding a new term to their agreement whereby an arbitrator they did not agree upon might decide their disputes.[6]
*362 On written agreement of the parties, a court may refer a suit affecting the parent-child relationship to arbitration. Tex. Fam. Code Ann. § 153.0071(a) (Vernon 2002). The method of appointing an arbitrator is as specified in the agreement to arbitrate. Tex. Civ. Prac. & Rem.Code Ann. § 171.041(a) (Vernon Supp.2004). However, if an agreement to arbitrate does not specify a method of appointment, or the agreed method fails or cannot be followed, the court shall appoint an arbitrator upon application of a party. Id. § 171.041(b)(1), (2).
Contrary to Lynn's position, the failure to identify an arbitrator, or even specify a method for choosing one, does not render an arbitration agreement unenforceably incomplete. See id. Moreover, to the extent a binding arbitration agreement existed, as Lynn acknowledges and the trial court expressly concluded,[7] the language inserted by the trial court merely reflects the law applicable to the agreement and, thus, did not add a material term to it. Although Lynn urges a different interpretation of the arbitration provision that would defeat its effect as a binding arbitration agreement, she has cited no authority or rationale to overcome the trial court's determination to the contrary. Under these circumstances, her second issue affords no basis for relief and is overruled. Accordingly, the judgment of the trial court is affirmed.
NOTES
[1]  The decree states that "a judgment lien is created and established against all community property herein awarded to Lynn as community property. This lien is in the nature of a purchase-money lien." After listing the items of property subject to this lien, the decree states, "the judgment lien herein imposed shall be a judicially imposed owelty lien with respect to the homestead real property of Lynn...."
[2]  See Tex. Fam.Code Ann. § 4.102 (Vernon Supp.2004) (allowing spouses to partition or exchange between themselves any part of their community property and thereby transform such property into a spouse's separate property).
[3]  See Tex. Fam.Code Ann. §§ 7.001, 7.006(a), (b) (Vernon 1998); Byrnes v. Byrnes, 19 S.W.3d 556, 559 n. 2 (Tex.App.-Fort Worth 2000, no pet.).
[4]  See Cameron v. Cameron, 641 S.W.2d 210, 213-15 (Tex.1982) (recognizing that the Texas Constitution and Family Code do not allow a court, in a divorce proceeding, to divest one spouse of separate property by awarding it to the other spouse). Lynn does not assert grounds to contest the imposition of the lien if the MSA was not a partition agreement.
[5]  See Byrnes, 19 S.W.3d at 559 (observing that Texas courts have refused to recognize transactions between spouses as partitions absent the use of that term or other language specifically indicating such an intent).
[6]  Lynn does not, however, contend that the arbitration provision of the MSA was ambiguous or otherwise uncertain and that it should, thus, have simply been left in that condition by the trial court for a possible later determination, if necessary.
[7]  The trial court's eighth and fifteenth findings of fact state, respectively, "The parties in the MSA entered into an arbitration agreement to settle specific future disputes," and "Any finding of fact that is a conclusion of law shall be deemed a conclusion of law." The trial court's ninth conclusion of law correspondingly states, "It is appropriate upon the application of a party for the Court to appoint an arbitrator when the parties can not agree upon an arbitrator but have agreed by a written and signed agreement that a dispute shall be arbitrated."
