  We investigate the renormalization of the quark-mixing matrix in the
Electroweak Standard Model. We show that the corresponding counterterms must be
gauge independent as a consequence of extended BRS invariance. Using rigid
SU(2)_L symmetry, we proof that the ultraviolet-divergent parts of the
invariant counterterms are related to the field renormalization constants of
the quark fields. We point out that for a general class of renormalization
schemes rigid SU(2)_L symmetry cannot be preserved in its classical form, but
is renormalized by finite counterterms. Finally, we discuss a genuine physical
renormalization condition for the quark-mixing matrix that is gauge independent
and does not destroy the symmetry between quark generations.
