The study of piecewise maps have been given extensive attention, because these maps represent a large number of engineering systems with nonsmooth vector fields.In such maps.a new class of bifurcations can occur when a fixed point collides with the borderline between smooth regions, which was coined the term "border collision bifurcation"[1].Basically the study on border collision bifurcations have been done using the piecewise linear approximation at the two sides of the border[2].