  We provide a complete and systematic analysis of hermitian, hierarchical
quark mass matrices with four texture zeros. Using triangular mass matrices,
each pattern of texture zeros is readily shown to lead to a definite relation
between the CKM parameters and the quark masses. Nineteen pairs are found to be
consistent with present data, and one other is marginally acceptable. In
particular, no parallel structure between the up and down mass matrices is
found to be favorable with data.
