A transfer function form, in thezdomain, of the discrete time stationary algebraic Riccati equation is investigated. A discrete generalized spectral factorization technique that copes with unstable plants is introduced. This factorization is used to provide an efficient way for solving the Riccati equation and the proposed method is easily extended to cope, in the filtering problem, with coloured signals. The superiority of its computational method for systems having a small number of inputs and outputs is discussed.