  We look for all weak bases that lead to texture zeroes in the quark mass
matrices and contain a minimal number of parameters in the framework of the
standard model. Since there are ten physical observables, namely, six
nonvanishing quark masses, three mixing angles and one CP phase, the maximum
number of texture zeroes in both quark sectors is altogether nine. The nine
zero entries can only be distributed between the up- and down-quark sectors in
matrix pairs with six and three texture zeroes or five and four texture zeroes.
In the weak basis where a quark mass matrix is nonsingular and has six zeroes
in one sector, we find that there are 54 matrices with three zeroes in the
other sector, obtainable through right-handed weak basis transformations. It is
also found that all pairs composed of a nonsingular matrix with five zeroes and
a nonsingular and nondecoupled matrix with four zeroes simply correspond to a
weak basis choice. Without any further assumptions, none of these pairs of up-
and down-quark mass matrices has physical content. It is shown that all
non-weak-basis pairs of quark mass matrices that contain nine zeroes are not
compatible with current experimental data. The particular case of the so-called
nearest-neighbour-interaction pattern is also discussed.
