The Tevatron BPM Upgrade Project will improve the current Tevatron BPM system, and part of the improvement will insure reliable pbar beam position measurements in the presence of protons. This paper discusses a method for de-embedding the proton signal that leaks through to the pbar end of the pickup and vice versa. The paper derives the linear relationship between the proton signal on the proton side of the pickup and the proton signal on the pbar side of the pickup for an ideal situation. It then discusses the effects of different non-idealities in the presence of real beam.