  We study the renormalized Coulomb interactions due to retardation effect in
Na$_x$CoO$_2$. Although the Morel-Anderson's pseudo potential for $a_{1g}$
orbital $\mu^*_{a1g}$ is relatively large because the direct Coulomb repulsion
$U$ is large, that for interband transition between $a_{1g}$ and $e_g'$
orbitals $\mu^*_{a1g,eg'}$ is very small since the renormalization factor for
pair hopping $J$ is square of that for $U$. Therefore, the s-wave
superconductivity due to valence-band Suhl-Kondo mechanism will survive against
strong Coulomb interactions. The interband hopping of Cooper pairs due to shear
phonons is essential to understand the superconductivity in Na$_x$CoO$_2$.
