  We present a new efficient method for computing the non-linearity parameters
of the higher order correlation functions of local type curvature perturbations
in inflation models having a $\cal N$-component scalar field, focusing on the
non-Gaussianity generated during the evolution on super-horizon scales. In
contrast to the naive expectation that the number of operations necessary to
compute the $n$-point functions is proportional to ${\cal N}^n$, it grows only
linearly in ${\cal N}$ in our formalism. Hence, our formalism is particularly
powerful for the inflation models composed of a multi-component scalar field.
Explicit formulas obtained by applying our method are provided for $n=2,3,4$
and 5, which correspond to power-, bi-, tri- and {\it quad}-spectra,
respectively. We also discuss how many parameters we need to parameterize the
amplitude and the shape of the higher order correlation functions of local
type.
