  The Coulomb pseudo-potential $\mu^*$ is extracted by fitting the numerically
calculated transition temperature $T_c$ of the Eliashberg-Nambu equation which
is extended to incorporate the narrow-band effects, that is, the vertex
correction and the frequency dependence of the screened Coulomb interaction. It
is shown that even for narrow-band superconductors, where the fermi energy $
\epsilon_F$ is comparable with the phonon frequency $ \omega_{ph}$, the Coulomb
pseudo-potential is a pertinent parameter, and is still given by $\mu^* =
\mu/[1+\mu \ln(\epsilon_F/\omega_{ph})] $, provided $\omega_{ph}$ is
appropriately scaled.
