  We study the inverse Compton scattering of the CMB photons off nonthermal
high-energy electrons. In the previous study, assuming the power-law
distribution for electrons, we derived the analytic expression for the spectral
intensity function $I(\omega)$ in the Thomson approximation, which was
applicable up to the photon energies of $\omega <$ O(GeV). In the present
paper, we extend the previous work to higher photon energies of $\omega >$
O(GeV) by taking into account the terms dropped in the Thomson approximation,
i.e., the Klein-Nishina formula. The analytic expression for $I(\omega)$ is
derived with the Klein-Nishina formula. It is shown that $I(\omega)$ has a
"knee" structure at $\omega =$ O(PeV). The knee, if exists, should be
accessible with gamma-ray observatories such as Fermi-LAT. We propose simple
analytical formulae for $I(\omega)$ which are applicable to wide photon
energies from Thomson region to extreme Klein-Nishina region.
