This note presents a new algorithm for the division of two polynomial matrices, consisting of a modification of the algorithm shown by Q. Wang and C. Zhou [ibid. AC-31, 165-166 (1986; Zbl 0587.65034)]. We improve the performance of their algorithm by means of the use of convolutions, and therefore of FFT techniques. Our method is based on the fast inversion of block triangular Toeplitz matrices, and is amenable for parallel implementation.