Arbitrary design specifications often result in conflicting requirements, which are physically mutually exclusive. By restricting the design objective to equiripple response in the passband, the paper develops a method that accommodates the natural properties of the multilayer. This is accomplished by allowing the passband transmittance maxima and minima of a fixed-index multilayer to settle in their equilibrium positions appropriate to its physical nature. Transmittance adjustment takes place at the passband extremes, which are continually tracked during the refinement process, hence the name turning point method. Control of transmittance at these key points ensures wideband capability for both lowpass and highpass filters. The multilayers thus designed are optimum in the Chebychev sense.