A way is proposed to make multilayer dielectric mirrors with unusual dependence of reflection phase on frequency, dΨ/dω > 0. Simultaneously, the reflection amplitude can be nearly unity. The method of calculation is based on the theory of reflecting interferometers. The resulting multilayer structure can be a starting point for further refinement by the usual optimization methods. The mirrors can be used in a dispersion-free Fabry-Perot interferometer, which is insensitive to frequency deviations of a light source.