  We calculate the quantized conductance of nanosize point contacts between two
ferromagnets for different mutual orientations of the magnetic moments. It is
found that the magnetoresistance MR is a multivalued function of the quantized
conductance at the parallel alignment of the magnetizations sigma^F. This leads
us to the conclusion that experimentally observed large fluctuations of MR
versus sigma^F are rather due to the conductance quantization than to
measurement errors or a poor reproducibility of the results. Using the results
of the calculations we are able to understand experimental data obtained by
Garcia et al for MR of the magnetic nanocontacts.
