For the non-Hermitian Fritzsch-type mass matrix (M̃u, M̃d), which is a general expression of quark mass matrices, the rephasing-gauge dependency and δ-dependency (where Vub = |Vub|e) of each matrix element M̃qij (q = u, d; i, j = 1, 2, 3) are investigated. We find that the textures of (M̃u, M̃d) depend on the rephasing gauge and we can always take M̃u32 = 0 without losing generality, so that the rema...