  Let $\mathfrak M$ and $\mathfrak N$ be separable Hilbert spaces and let
$\Theta(\lambda)$ be a function from the Schur class ${\bf S}(\mathfrak
M,\mathfrak N)$ of contractive functions holomorphic on the unit disk. The
operator generalization of the classical Schur algorithm associates with
$\Theta$ the sequence of contractions (the Schur parameters of $\Theta$)
$\Gamma_0=\Theta(0)\in \bL(\sM,\sN), \Gamma_n\in\bL(\sD_{\Gamma_{n-1}},
\sD_{\Gamma^*_{n-1}}) $ and the sequence of functions $\Theta_0 = \Theta$,
$\Theta_n\in {\bf S}(\sD_{\Gamma_n},\sD_{\Gamma^*_n})$ $ n=1,...$ (the Schur
iterares of $\Theta$) connected by the relations
  \[ \Gamma_n=\Theta_n(0), \Theta_n(\lambda) = \Gamma_n+\lambda D_{\Gamma^*_n}
\Theta_{n+1}(\lambda) (I + \lambda\Gamma^*_n\Theta_{n+1}
(\lambda))^{-1}D_{\Gamma_n}, |\lambda|<1. \]
  The function $\Theta(\lambda)\in {\bf S}(\sM,\sN)$ can be realized as the
transfer function
  \[ \Theta(\lambda)=D+\lambda C(I-\lambda A)^{-1}B \] of a linear conservative
and simple discrete-time system $\tau = {\begin{bmatrix}D & C \cr B &
A\end{bmatrix}; \mathfrak M, \mathfrak N,\mathfrak H}$ with the state space
$\mathfrak H$ and the input and output spaces $\mathfrak M$ and $\mathfrak N $,
respectively. In this paper we give a construction of conservative and simple
realizations of the Schur iterates $\Theta_n$ by means of the conservative and
simple realization of $\Theta$.
