As it has been proved by Kohn, the ground state density is unique even for systems, where frontier orbitals are degenerate. The simple practical method has been applied to circumvent another well-known difficulty in reproducing spherical symmetry of the electron density in atoms. Two steps have been involved in this procedure. Integration of the electron density has been routinely made by the spherical algorithm for a density variable in one direction only. The result of integration to proper number of electrons served as evidence of a spherical symmetry of the density. For atoms whose basic electronic terms were other that S type, the numerical averaging procedure over principal coordinate axis and all diagonal directions has been applied