A software package was designed and used in a detailed study of the contact regions (interfaces) of a large number of protein-protein complexes using the PDB data. It appeared that for about 75% of the complexes the amino acid composition of the subunit surface in the contact region is not essential. Thus one may suggest that, along with the amino acid residues at the interface, the residues in the interior of the globules substantially contribute to protein-protein recognition. Such interactions between quite remote residues are most probably of electrical nature, and are involved in recognition by contributing to the overall electric field created by the protein molecule; the configuration of this field is perhaps the definitive factor of recognition. The overall field of the protein molecule is additively built of the fields created by each constituent residue, and it can be calculated as a sum of the fields created by the protein multipole (aggregate of 'partial' electric charges assigned to every atom of the protein molecule). Preliminary calculations of the remote electrostatic interaction have been performed for ribonuclease subunits in vacuum. The results are indicative of a real possibility that the electric field created by the protein multipole can strongly influence the mutual orientation of molecules before Brownian collisions.