  We analyze statistical properties of complex eigenvalues of random matrices
$\hat{A}$ close to unitary. Such matrices appear naturally when considering
quantized chaotic maps within a general theory of open linear stationary
systems with discrete time. Deviation from unitarity are characterized by rank
$M$ and eigenvalues $T_i, i=1,...,M$ of the matrix $\hat{T}=\hat{{\bf
1}}-\hat{A}^{\dagger}\hat{A}$. For the case M=1 we solve the problem completely
by deriving the joint probability density of eigenvalues and calculating all
$n-$ point correlation functions. For a general case we present the correlation
function of secular determinants.
