This paper presents a new method for factoring a self‐inversive Hermitian matrix polynomial relative to the unit‐radius circle. It formulates the factorization problem as that of evaluating a set of definite integrals along the unit circle and of solving a block‐Toeplitz system of linear equations. Since the evaluation of definite integrals along the unit circle can be accomplished via parallel computations and the solution of a block‐Toeplitz system can be obtained by a fast algorithm, the proposed method is very useful in real‐time applications.