An efficient method for computing diffraction integrals is presented. It is based on an idea put forward by Hopkins [1]. The integration domain is divided into subdomains, in each of which the phase and amplitude are approximated by simple functions which make it possible to evaluate the resulting integral in terms of known functions. While Hopkins employed a linear approximation to the phase and a constant approximation to the amplitude, we here approximate both the phase and the amplitude by parabolas. A comparison of the results of our method with those of Hopkins's method shows that our method requires fewer subdomains and less computation time to yield a desired accuracy. Another advantage of our method is that it can be applied to apertures of a general shape without significant loss of accuracy.