A model of quark masses and mixing angles is constructed within the framework of two large extra compact dimensions. A "democratic" almost pure phase mass matrix arises in a rather interesting way. This type of mass matrix has often been used as a phenomenologically viable ansatz, albeit one which had very little dynamical justification. It turns out that the idea of large extra dimensions provides a fresh look at this interesting phenomenological ansatz as presented in this paper. Some possible interesting connections to the strong CP problem will also be presented. (C) 2003 Elsevier Science B.V. All rights reserved.