We develop a systematic analysis of quark mass matrices which, startin
g with the measured values of quark masses and mixing angles, allows f
or a model-independent search for all possible (symmetric or hermitian
) mass matrices having texture zeroes at the unification scale. A surv
ey of all six and five texture zero structures yields a total of five
possible solutions which may be distinguished by improved measurements
of the CKM matrix elements and which may readily be extended to inclu
de lepton masses with the Georgi-Jarlskog texture. The solutions natur
ally suggest a parameterisation for the mass matrices based on a pertu
rbative expansion and we present some speculations concerning the orig
in of such structure.