Аннотация:Some precautions to the measurements of weak stellar magnetic fields by the least squares technique are considered on the example of Cyg X-1 = HDE 226868 (the optical counterpart is an O9.7 supergiant). The V/I circular polarization spectra obtained during our spectropolarimetric FORS1 VLT observations have variable sloped continuum components not belonging to the object. It is shown that such components should be removed, otherwise these spurious sloped continua yield biased results. For HDE 226868 the magnetic field bias Δ\ltB_z\gt varies from 20 G to 100 G, which is comparable to its value. The slopes of the I-spectra have a smaller influence on \ltB_z\gt result but they should be subtracted too. Initial I and V/I-spectra cleaning, the effects from the deviating points and their influence on the results of \ltB_z\gt measurements are also considered.