  In this paper we suggest a new approach for the multichannel Coulomb
scattering problem. The Schr\"{o}dinger equation for the problem is
reformulated in the form of a set of inhomogeneous equations with a
finite-range driving term. The boundary conditions at infinity for this set of
equations have been proven to be purely outgoing waves. The formulation
{presented here} is based on splitting the interaction potential into a finite
range core part and a long range tail part. The conventional matching procedure
coupled with the integral Lippmann-Schwinger equations technique are used in
the formal theoretical basis of this approach. The reformulated scattering
problem is suitable for application in the exterior complex scaling technique:
the practical advantage is that after the complex scaling the problem is
reduced to a boundary problem with zero boundary conditions. The Coulomb wave
functions are used only at a single point: if this point is chosen to be at a
sufficiently large distance, on using the asymptotic expansion of Coulomb
functions, one may completely avoid the Coulomb functions in the calculations.
The theoretical results are illustrated with numerical calculations for two
models.
