  We analyse an effect of electron Fermi motion at atomic shells on the
accuracy of electron beam polarization measurements with a M\"oller polarimeter
operating in a double--arm mode. It is demonstrated that the effect can result
in either {\it increase} or {\it decrease} of the measured polarization
depending on the detector positions. The effect is simulated for the M\"oller
polarimeter to be installed at CEBAF Hall A.
