This preprint represents the original notes of the authors (SSPJU 6/76, October 1976), which were published later (K. A. Chao, J. Spałek, and A. M. Oleś, J. Phys. C: Sol. St. Phys. 10, L271-L276 (1977)) in a modified form. The preprint is supplemented (1977) with one-page elaboration of the results in the spin-rotationally invariant form, which was used in later publications (cf. J. Spałek et al., Phys. Stat. Sol. (b) 108, 329 (1981)).

We use the canonical transformation method in the Hubbard model to derive the general form of the effective Hamiltonian which includes the virtual hopping from single- to double-occupied sites. The correspondence with the Anderson kinetic exchange Hamiltonian is briefly discussed.