2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/49115A direct proof is given here which shows that instead of 6 complex numbers, the triangular mass matrix for each sector could just be expressed in terms of 5 by performing a specific weak basis transformation, leading therefore to a new textures for triangular mass matrices. Furthermore, starting with the set of 20 real parameters for both sectors, it can shown that 6 redundant parameters can be removed by using the rephasing freedom.8 pages, latex; Submitted to Phys. Lett. BHigh Energy Physics - Phenomenologytext