  We investigate, using a $1/N$ expansion, the behavior of a parameter in the
scalar--fermion sector of the standard model that shows perturbative
non--decoupling as the fermion becomes heavy. This low energy parameter is
related to the $S$ parameter defined through the $W_3-B$ vacuum polarization
tensor. We obtain the leading $1/N$ contribution to this parameter that, if
expanded perturbatively, collapses to its constant one--loop result; remarkably
all the higher--order terms in the series vanish. Non--perturbatively, however,
we find that as the mass of the fermion approaches the built--in cutoff scale
of the theory --- the triviality scale --- the parameter is highly dependent on
the implementation of the cutoff; it is non--universal, and shows
non--decoupling.
