We consider the factorization of an all-pass matrix function E(s) into proper, stable, minimum-phase factors. This is achieved by applying the state-space Wiener-Hopf factorization theory of Bartet al. (1983) to the state-space characterization of all-pass matrix functions given by Glover (1984). Important connections are made between the properties of E( s) as a Nehari extension, its partial Wiener-Hopf factorization indices, and its Hankel singular values.