Abstract: The Iterated Function System (IPS) is an important theoretic and applied branch of fractal geometry. An IPS defines a point set called the attractor, but there have not any effective methods to obtain the corresponding IPS of a given point set. This paper first proposes an approach to constructing a function for a finite point set defined on the one-dimensional line, so the problem of determining the coefficinets of the affine transformation in an IPS is transfered into determining the extreme points of a the function. This method is then, extended to the two-dimesional plane.