A variant of Brosche's well-known method is proposed which allows one to represent systematic differences (many times faster than with the original method) by the use spherical harmonics. The improved economy of computer memory requirements and reduction of calculating time are achieved by replacing the two-arguments approximation with a sequence of one-argument approximations, and by enforcing an equidistant distribution of the initial differences along the α and the δ directions. The proposed method was tested on models and used for representing the systematic corrections Δ δα and Δ μα to the catalogues GC and N30.