  An asymptotically exact result is obtained for the renormalized phonon energy
as a function of the on-site Coulomb repulsion $U_{ee}$ in the half-filled
Hubbard-Holstein model in the strong-coupling region at zero temperature. The
result is obtained on the basis of the effective Hamiltonian derived in the
antiadiabatic region with due attention to the transition from CDW- to
SDW-regime with the increase of $U_{ee}$. Somewhat contrary to naive
expectation, the phonon energy is found to shift in the insulating phase and
the shift becomes larger in the SDW regime than that in the CDW regime.
