The Milne problem for isotropic scattering for one speed and for the conservative case, (c = 1), is solved by using the full-range completeness property of Case’s eigenfunctions. Explicit numerical results are derived by iterating on a very rapidly convergent Fredholm integral equation, and the results thus obtained are in excellent agreement with those obtained previously by the use of Case’s half-range completeness theorem. Since for multigroup formulations the full-range completeness is more easily proved (as compared to the half-range completeness), it is felt that the present approach may prove useful.