  The asymptotic wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A
47, 2004 (1993)] and Mukhamedzhanov and Lieber [Phys. Rev. A 54, 3078 (1996)]
has been refined in the region where the pair $ (\beta,\gamma)$ remains close
to each other while the third particle $\alpha$ is far away from them
$(\rho_{\alpha} \to \infty$, $r_{\alpha}/\rho_{\alpha}\to 0)$. The improved
wave function satisfies the Schr\"odinger equation up to the terms of order
$O(1/{\rho_{\alpha}}^{3})$, provides the leading asymptotic terms of the
three-body scattering wave function with Coulomb interactions and gives further
insight into the continuum behavior of the three-charged-particle wave function
and helps to obtain $3\to 3$ scattered wave. This opens up further ways of
solving and analysing the three-body Schr\"odinger equation by numerical means.
