We extend a new stability test proposed recently for discrete system polynomials [1] to polynomials with complex coefficients. The method is based on a three-term recursion of a conjugate symmetric sequence of polynomials. The complex version has the same relative improved efficiency as the real version in comparison to the classical Schur-Cohn formulation for counting the number of zeros of a polynomial with respect to the unit circle. Furthermore, if desirable, the complex text can be carried out using only real polynomials and arithmetic.