  We propose a new and simple On-Shell definition of off-diagonal fermion field
and mass counterterms at 1-loop in terms of self-energy scalar functions.
Further, we show that the anti-hermitian part of the field renormalization is
always finite and that mass counterterms can be chosen gauge-independent. It is
noteworthy that our definition relies on mass structures, which is a novel
approach, and does not require to drop absorptive parts as is usually the case.
Definitions of the off-diagonal mass and field counterterms allow us to comment
on the renormalization of mixing matrices with focus on the quark mixing matrix
in the Standard Model. As an example of our scheme, we provide computations in
the Two Higgs Doublet Model with an additional Heavy Majorana neutrino - the
Grimus-Neufeld model. This allows for the comparison with other schemes known
in literature and also provides examples for the case of massless fermions. The
examples also serve as genuine results in this particular model as well as this
scheme. In the appendix the scheme is extended to arbitrary orders, although
without example computations in the Grimus-Neufeld model.
