  We study the one-loop effective potential induced from quantum fluctuation of
a finite number of fields. A series expansion in terms of the modified Bessel
functions is useful to evaluate the one-loop effective potential. We find that
at most $N-2$ scalars parameterize the one-loop finite potential and the
explicit parameterization is shown. The structure of the potential for N=4 is
investigated as the simplest case. The implication of the model is discussed.
