In a proceeding pursuant to CPLR article 75 to stay arbitration, the petitioner appeals (1) from an *65order of the Supreme Court, Nassau County (Brucia, J.), dated September 25, 1986, which dismissed the petition, and (2) as limited by its brief, from so much of an order of the same court dated February 24, 1987, as, upon reargument, adhered to the prior determination.
Ordered that the appeal from the order dated September 25, 1986, is dismissed, without costs or disbursements, as it was superseded by the order dated February 24, 1987, made upon reargument; and it is further,
Ordered that the order dated February 24, 1987, is reversed insofar as appealed from, on the law, without costs or disbursements, the order dated September 25, 1986, is vacated, and the petition to stay arbitration is granted.
Daniel Reilly is the legal representative of Mary Reilly, who died as the result of injuries suffered in an automobile accident which occurred on February 21, 1985. The petitioner Continental Insurance Company subsequently paid Mr. Reilly $50,000 pursuant to the uninsured motorist endorsement which was contained in a policy of insurance applicable to the Reilly vehicle. Mr. Reilly thereafter demanded arbitration of his claim that he was entitled to collect additional sums pursuant to the "underinsured motorist coverage” provided for in the policy. The petitioner made an application to stay arbitration on the basis that its underinsured motorist endorsement did not provide coverage in this case. The Supreme Court denied this application. We reverse, and grant the application.
Pursuant to the underinsured motorist coverage contained in its policy, the petitioner promised to pay, subject to certain limits, "damages which a covered person is legally entitled to recover from the owner or operator of an underinsured motor vehicle”. The term "underinsured motor vehicle” is defined so as to be limited to vehicles "to which a bodily injury liability bond or policy applies at the time of the accident”. The petitioner claims that the vehicle with which the Reilly vehicle collided was not insured at all and this assertion is not denied in the respondent’s affirmation in opposition to the original petition or in the affirmation in opposition to the motion for reargument. Thus, it is clear that the offending vehicle in the present case was uninsured, rather than "underinsured” within the meaning of the petitioner’s policy, so that the underinsured motorist coverage is, by its terms, inapplicable.
Furthermore, there is nothing in the law which would *66permit this court to rewrite the parties’ agreement so as to make the petitioner’s underinsured motorist coverage applicable to this case, regardless of its unambiguous language. Insurance Law § 3420 (f) (2) requires insurers to offer supplementary uninsured, motorist coverage, and such coverage must, if purchased, also provide what is commonly referred to as underinsured motorist coverage. Many policies are apparently written so as to include underinsured motorist coverage within the broader definition of supplementary uninsured motorist coverage (see generally, Reichel v Government Employees Ins. Co., 107 AD2d 463, affd 66 NY2d 1000). However, this statute does not prohibit an insurer from writing a policy which contains underinsured motorist coverage only, without concomitantly providing supplementary uninsured motorist coverage. The underinsured motorist coverage provided in the petitioner’s policy may therefore properly be limited to situations involving underinsured, but not uninsured, vehicles. This is the sort of underinsured motorist coverage which "presupposes that the offending vehicle has liability insurance coverages for at least the minimal amount of coverage required by law” (Matter of United Community Ins. Co. v Mucatel, 127 Misc 2d 1045, 1046, affd 119 AD2d 1017, rearg denied 121 AD2d 357, affd 69 NY2d 777).
Accordingly, since the terms of the underinsured motorist coverage endorsement are unambiguous, and since such coverage is clearly not available in the present case, the petitioner’s motion to stay arbitration should have been granted. Mangano, J. P., Bracken, Eiber and Kunzeman, JJ., concur.