New necessary and sufficient conditions for a real polynomial to have all its zeros inside the unit circle are derived. The conditions are obtained by the study of certain new forms of z-domain continued fraction expansions. They induce an effective procedure for testing the stability of discrete systems that reminds in many ways the Routh scheme for Hurwitz polynomials. A table form is also presented for the stability criterion. The table has half the size and involves half the amount of computation of the Jury-Marden table.