  It is shown that monic orthogonal polynomials on the unit circle are the
characteristic polynomials of certain five-diagonal matrices depending on the
Schur parameters. This result is achieved through the study of orthogonal
Laurent polynomials on the unit circle. More precisely, it is a consequence of
the five term recurrence relation obtained for these orthogonal Laurent
polynomials, and the one to one correspondence established between them and the
orthogonal polynomials on the unit circle. As an application, some results
relating the behavior of the zeros of orthogonal polynomials and the location
of Schur parameters are obtained.
