We calculate the quantized conductance of nanosize point contacts between twoferromagnets for different mutual orientations of the magnetic moments. It isfound that the magnetoresistance MR is a multivalued function of the quantizedconductance at the parallel alignment of the magnetizations sigma^F. This leadsus to the conclusion that experimentally observed large fluctuations of MRversus sigma^F are rather due to the conductance quantization than tomeasurement errors or a poor reproducibility of the results. Using the resultsof the calculations we are able to understand experimental data obtained byGarcia et al for MR of the magnetic nanocontacts.
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