This paper presents a technique for calculating cross sections of excitation of atoms by fast electrons. To do this a technique of expansion over partial wave functions taking into account the antisymmetric properties of the wave function, is used. The scattering operator takes into account spin-dependent interactions. Using Born approximation we have calculated a cross section of the intercombination transition 11S - 33S of helium atoms. Calculational results show that at energies of electrons about 10 keV and above the corrections of the scattering operator for relativistic effects should be done.