A new layer-by-layer multilayer design method is presented. The method is demonstrated mathematically and makes possible the optimization of the multilayer for the highest possible reflectance either at normal incidence or at nonnormal incidence for s- or p-polarized radiation. With the current method multilayers can be designed regardless of the number of different materials used. The optimum layer thickness is determined by means of functions suitable for implementation in a computer code. The new multilayer design method is fast and accurate.