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NASA's Solar Dynamics Observatory is delivering vector field observations of the full solar disk with unprecedented temporal and spatial resolution; however, the satellite is in a highly inclined geostationary orbit. The relative spacecraft-Sun velocity varies by $\pm3$~km/s over a day which introduces major orbital artifacts in the Helioseismic Magnetic Imager data. We demonstrate that the orbital artifacts contaminate all spatial and temporal scales in the data. We describe a newly-developed three stage procedure for mitigating these artifacts in the Doppler data derived from the Milne-Eddington inversions in the HMI Pipeline. This procedure was applied to full disk images of AR11084 to produce consistent Dopplergrams. The data adjustments reduce the power in the orbital artifacts by 31dB. Furthermore, we analyze in detail the corrected images and show that our procedure greatly improve the temporal and spectral properties of the data without adding any new artifacts. We conclude that this new and easily implemented procedure makes a dramatic improvement in the consistency of the HMI data and in its usefulness for precision scientific studies.