  The energy eigenvalue problem of non-relativistic positronium is considered
within the framework of Relativistic Schroedinger Theory (RST), and the results
are compared to those of the conventional quantum theory. For the range of
princi- pal quantum numbers n = 2;3;::: ;30, the RST predictions for the
non-relativistic positronium energies deviate now from the corresponding
predictions of the conven- tional quantum theory at an average of (roughly) 3%.
These results suggest that the deviations will be further diminished in the
higher orders of approximation.
