  In this note, we solve an inverse spectral problem for a class of finite band
symmetric matrices. We provide necessary and sufficient conditions for a matrix
valued function to be a spectral function of the operator corresponding to a
matrix in our class and give an algorithm for recovering this matrix from the
spectral function. The reconstructive algorithm is applicable to matrices which
cannot be treated by known inverse block matrix methods. Our approach to the
inverse problem is based on the rational interpolation theory developed in a
previous paper.
