  We propose here an alternative interpretation of the fermi-linarization
approach to interacting electron systems, based on the requirement that the
coefficients of the linearized operators are Clifford-like variables, whose
anticommutator equals an unknown constant $c$. We apply the approximation to
the Falicov-Kimball model, explicitly solving the self-consistency equation for
the unknown, which turns out to behave as an order parameter. We discuss its
relation with a metal-insulator transition and some thermodynamical quantities.
In particular we show that our approximation in the $T=0$ limit reproduces
exactly the Gutzwiller results for the Hubbard model.
