  We study the properties of heavy fermions in the vector-like representation
of the electro-weak gauge group $SU(2)_W\times U(1)_Y$ with Yukawa couplings to
the standard model (SM) Higgs boson. Using the renormalization group analysis,
we discuss their effects on the vacuum stability and the triviality bound on
the Higgs self-coupling, within the context of the standard model (i.e., the
Higgs particle is elementary). Contrary to the low energy case where the
decoupling theorem dictates their behavior, the inclusion of heavy fermions
drastically change the SM structure at high scale. We also discuss the
interesting possibility of compositeness, i.e., the Higgs particle is composed
of the heavy fermions using the method of Bardeen, Hill and
Lindner~\cite{BHL91}. Finally we briefly comment on their possible role in
explaining $R_b$ and $R_c$.
