  A modified Fritzsch ansatz for the quark mass matrices is proposed to account
for the hierarchical structure of the CKM matrix. To allow for the observed CP
asymmetry, restrictions have to be imposed on the relative phase degree of
freedom among the weak eigenstates of the quark fields, as for example by
certain additional symmetries. The ansatz can be accommodated in extensions to
the Standard Model, such as the multiple Higgs doublets models.
