Let V (z) = ∏ j = 1 m (z - ζ j), ζ h ≠ ζ k, h ≠ k and | ζ j | = 1, j = 1, ..., m, and consider the polynomials orthogonal with respect to | V | 2 d μ, φ n (| V | 2 d μ ; z), where μ is a finite positive Borel measure on the unit circle with infinite points in its support, such that the reciprocal of its Szego{combining double acute accent} function has an analytic extension beyond | z | < 1. In this paper we deduce the asymptotic behaviour of their Verblunsky coefficients. By means of this result, an asymptotic representation for these polynomials inside the unit circle is also obtained. © 2006 Elsevier Inc. All rights reserved.