A user-friendly divide-and-conquer algorithm is presented for finding all the self intersection points of a parametric curve in the Bernstein-Bezier representation. The underlying idea of the algorithm is to deal with the Bexier polygon instead of the curve description itself. By alternately subdividing the Bezier polygon and estimating the self intersection regions the self intersection points are finally approximated by straight line intersections of the refined Bezier polygons. The algorithm also calculates the parameter values of the self intersection points. In addition to the convex hull and the approximation property of the Bezier polygon the working of the algorithm is based on a very intuitive angle criterion. Keywords: Bezier curves; Spline curves; Intersection.