  Random band matrices relevant for open chaotic systems are introduced and
studied. The scattering model based on such matrices may serve for the
description of preequilibrium chaotic scattering. In the limit of a large
number of open channels we calculate the average $S$-matrix and $S$-matrix's
pole distribution which are found to reduce to those of the full matrix (GOE)
case under proper renormalization of the energy scale and strength of coupling
to the continuum.
