ABSTRACT: A way of counting free parameters in the quark mass matrices of the standard model, including the constraints coming from weak basis transformations, is presented; this allow to understand the exact physical meaning of the parallel and non-parallel texture zeros which appear in some “ans¨atz” of the 3 × 3 quark mass matrices, including the CP violation phenomena in the analysis, it is shown why the six texture zeros are ruled out. Finally, a five texture zeros “ans¨atze”which properly copes with all experimental constrains, including the angles of the unitary triangle, is presented.