  It is shown that a simple model of 2N-Grassmann variables with a four-body
coupling involves caustics when the integral has been converted to a bosonic
form with the aid of the auxiliary field. Approximation is then performed to
assure validity of the auxiliary field method(AFM). It turns out that even in
N=2, the smallest case in which a four-body interaction exists, AFM does work
more excellently if higher order effects, given by a series in terms of
$1/N^{1/3}$ around a caustic and of 1/N around a saddle point, would be taken
into account.
