The non-relativistic transition T-matrix element for electron impact ionization of H-like has been calculated with starting from the formulation of Brauner,Briggs and Klar.The final state wavefunction involving three appropriate confluent hypergeometric functions considers all three two-body interactions on an equal footing and satisfies the proper Coulomb boundary conditions.The long range Coulomb interaction occurring in the initial channel has been taken into account properly.The T-matrix element,including four confluent hypergeometric functions,has been reduced to a three-dimensional integral in real space.The results are of use in a wide class of scattering problems.