  It is well known that an operator-valued function $\Theta$ from the Schur
class ${\bf S}(\mathfrak M,\mathfrak N)$, where $\mathfrak M$ and $\mathfrak N$
are separable Hilbert spaces, can be realized as the transfer function of a
simple conservative discrete time-invariant linear system. The known
realizations involve the function $\Theta$ itself, the Hardy spaces or the
reproducing kernel Hilbert spaces. On the other hand, as in the classical
scalar case, the Schur class operator-valued function is uniquely determined by
its so called "Schur parameters". In this paper we construct simple
conservative realizations using the Schur parameters only. It turns out that
the unitary operators corresponding to the systems take the form of five
diagonal block operator matrices, which are the analogs of
Cantero--Moral--Vel\'azquez (CMV) matrices appeared recently in the theory of
scalar orthogonal polynomials on the unit circle. We obtain new models given by
truncated block operator CMV matrices for an arbitrary completely non-unitary
contraction. It is shown that the minimal unitary dilations of a contraction in
a Hilbert space and the minimal Naimark dilations of a semi-spectral operator
measure on the unit circle can also be expressed by means of block operator CMV
matrices.
