A new minimax method for refining optical multilayer systems is presented. It minimizes the maximum deviation of the spectral transmittance from the desired specifications. These are assigned in such a general way that any shape can be approximated. The algorithm consists of iterating optimization steps that are obtained by developing the transmittance in the Taylor expansion versus the known parameters and solved by piecewise-linear programming. The investigation is limited to the design of losslessmultilayers with assigned refractive indices and undetermined thicknesses. Some minimax-refined designs are compared favorably with those reported in the literature.