  We study the renormalization of the fermion mixing matrix in the Standard
Model and derive the constraints that must be satisfied to respect gauge
invariance to all orders. We demonstrate that the prescription based on the
{\it on-shell} renormalization conditions is not consistent with the
Ward-Takahashi Identities and leads to gauge dependent physical amplitudes. A
simple scheme is proposed that satisfies all theoretical requirements and is
very convenient for practical calculations.
