A discrete wave mechanical treatment of the hydrogen atom is extended to deal with states involving nonzero angular momentum. Only the radial portions of the wave vectors are covered. It is predicted that there is a nonzero minimum distance between the electron and the nucleus; this threshold distance increases with increasing angular momentum. Appropriate finite difference equations are formulated. The states with angular momentum exhibit the same degeneracy as do corresponding energy levels obtained from solutions of Schrödinger's equation.