The origin of interband electron pairing, responsible for enhancing superconductivity, and the factors controlling its strength were examined. We show that interband electron pairing is a natural consequence of breaking down the Born-Oppenheimer approximation during electron-phonon interactions. Its strength is determined by the pair-state excitations around the Fermi surfaces that take place to form a superconducting state. Fermi surfaces favorable for the pairing were found, and the implications of this observation are discussed.Since the discovery of superconductivity in Hg at 4 K in 1911, [1] numerous studies have been carried out to find other superconductors with higher superconducting transition temperature T c and understand the cause for superconductivity. The charge carriers of superconductors are pairs of electrons while those of normal metals are individual electrons. The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity, [2] in which the electron pairing arises from electron-phonon interactions, showed that the T c increases with raising the average phonon frequency hwi of the lattice, the electronic density of states (DOS) at the Fermi level n(e F ) and the electron-phonon coupling constant l. By explicitly taking into consideration the actual electron-phonon interactions and the Coulomb repulsion between pairing electrons, Eliashberg extended the BCS theory to show the relationship of T c to the effective Coulomb repulsion m* and the electron-phonon spectral function a 2 (w) F(w). [3,4] McMillan numerically solved the Eliashberg equations as a function of m* and a 2 (w) F(w) in a small range of m* and l to express T c as an exponential function of l and m* with the prefactor V D /1.45, where V D is the Debye temperature. [5] The McMillan equation was improved by Allen and Dynes [6] by modifying the prefactor such that all parameters constituting the prefactor can be calculated once the spectral function a 2 (w) F(w) is known. Thus, with typical value of m* = 0.13, one can predict the T c of any metal on the basis of the Allen-Dynes