In the calculation of electron-atom cross sections it is often quite useful to obtain wave functions for the scattered particles which are orthogonal to the wave functions of the electrons bound in the atom. This constraint, although it may neglect certain couplings, provides a considerable simplification in obtaining certain transition matrix elements. A straightforward technique for enforcing this orthogonality condition is to include Lagrange multipliers in the differential equation. It has been found that depending on the values of the Lagrange multipliers there may be zero, one, or two solutions. However, the solution which yields orthogonality is unique. Non-iterative schemes for solutions are discussed and applied to electronhydrogen atom scattering.