We granted certiorari because this is a case of first impression in this Court. The Court of Civil Appeals correctly held in Insurance Company of North America v. Thomas, 337 So.2d 365 (Ala.Civ.App. 1976), that all motor vehicle liability insurance policies issued in this state would be construed as providing minimum uninsured motorist coverage mandated by § 32-7-23, Code 1975, unless a written agreement rejecting such coverage on the part of the named insured was shown.

The trial court in this case construed the policy to provide such coverage. There was no written rejection offered in evidence. The question, then, is whether the trial court was justified in finding that *430the insured had not rejected uninsured motorist coverage in writing. We have reviewed the record and are clear to the conclusion that the trial court had evidence before it from which it could find that no written rejection had been executed by the insured. To be sure, there was contrary evidence, but the trier of the fact was not bound to believe it. In this case, like all others where the trial judge is charged with making a determination of an issue of fact, he is free to make that determination, taking into account the probable bias of the witnesses, their demeanor while testifying, and may in doing so reject some evidence in favor of other evidence, and an appellate court must accept his determination unless clearly erroneous or manifestly unjust. Tanner v. Thompson, 376 So.2d 697 (Ala. 1979).

The Court of Civil Appeals, 409 So.2d 426, reversed the trial court’s judgment. Because the issue before the Court of Civil Appeals was purely a factual one and because there was evidence to support its finding, we reverse the judgment of the Court of Civil Appeals.

REVERSED AND REMANDED.