Development of centrifugal compressors consists of several steps, the most important of them being preliminary design. A variety of methods are applied for solving this problem. One of these methods was developed by Galerkin and Rekstin. However, this method did not fully resolve all issues and was not tested by practice. In addition to this method, we have proposed a technique for adjusting the relative height of impeller blades, taking into account Mach numbers and the isentropic coefficient. We have formulated an approach to determining the empirical coefficient for calculating the pressure characteristics of the impeller when solving for the direct problem that is calculating the characteristics of the stage with the dimensions determined by preliminary design. The presented changes were implemented in the program for preliminary design of centrifugal compressor stages. The effectiveness of primary design was tested with a program for inviscid quasi-three-dimensional calculation by verifying the shape of impeller blades. Three stages have been designed with different values of design parameters (loading factor and flow rate). Analysis of the velocity diagrams on impellers blades showed that they were designed according to the specified design parameters.