How interband pairing increases the superconductive transition temperature

The possible strong electron-phonon coupling and the pairing within the full width of the electron band and not only in a narrow sheet near the Fermi surface are taken into account. It is found that the effect of pairing of electrons belonging to different bands is crucial to the appearance of high Tc in some two-band materials. The existence of another set of the two-band high temperature materials with transition temperature Tc, not yielding Tc in cuprates, is predicted.