A new method is proposed for numerical solution the Coulomb two-center problem in continuum spectrum. The separation constants and angular Coulomb spheroidal functions are defined as the solutions of the generalized algebraic eigenvalue problem, which is approximated the Sturm–Liouville problem for angular functions by finiteelement method. For calculation the norms and phases of radial Coulomb spheroidal functions the boundary problem for radial functions is reduced to the problem with initial conditions for Milne equation. This conditions are accounted the quasi-classical asymptotic expansion of solution to infinity. The algorithms and programs are more effective then other analogous.