We generalize it recently proposed oil-shell approach to renormalize the Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of all 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. (C) 2009 Elsevier B.V. All rights reserved.