An extension to include general inelastic scattering effects is developed for the case of reflection electron diffraction scattering from surfaces. In this extension of work by Lynch and Moodie, it is shown how the resultant non-Hermitian matrix problem can be recast in a form that is suitable for computation. In particular, a computational method is outlined based on techniques developed by Eberlein for matrix diagonalisation using complex rotations and shears. The resultant methods are applied to the problem of Convergent Beam RHEED. 23 refs., 3 figs.