  Data accumulated from 0000 to 0000 with the Gamma RaySpectrometer aboard NASA's Solar Maximum Mission (SMM) satellite were searched for evidence of red and blue Doppler-shifted 0.00 MeV Mg-00 nuclear lines from SS 000. The SMM data base covers 000 days when SS 000 was in the field of view and includes periods of radio flaring and quiescence. No evidence was found for Doppler-shifted line emission in any of the spectra. The range of 0-sigma upper limits for individual 0 day integration periods was 0.0000-0.0000 photons/sq cm per sec for the blue beam, encompassing the reported about 0.0 MeV line, and 0.0000-0.000 photons/sq cm per sec for the red beam, encompassing the reported about 0.0 MeV line; the average 0-sigma upper limit in each beam for shifted about 0.00 MeV lines is 0.0000 photons/sq cm per sec for single 0 day integrations. The 0-sigma upper limit on 0.00 MeV gamma-ray emission over 00 0-day integration intervals for the red beam and 00 intervals for the blue beam is 0.0000 photons/sq cm per sec. These new limits from SMM can be reconciled with the HEAO 0 results only if SS 000 emits gamma radiation at or above the SMM sensitivity limit on rare occasions due to variable physical conditions in the system. 