  We generalize a recently proposed on-shell approach to renormalize the
Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of an extended
leptonic sector that includes Dirac and Majorana neutrinos in the framework of
the seesaw mechanism. An important property of this formulation is the gauge
independence of both the renormalized and bare lepton mixing matrices. Also,
the texture zero in the neutrino mass matrix is preserved.
