  The helicity amplitudes of the high-energy photon splitting in the external
Coulomb field are obtained exactly in the parameter $\al$. The cases of
screened and unscreened potentials are investigated. The consideration is based
on the quasiclassical approach, valid for small angles between all photon
momenta. New representation of the quasiclassical electron Green function is
exploited. General expressions obtained are analyzed in detail for the case of
large transverse momenta of both final photons compared to the electron mass.
