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 σF. This leads us to the conclusion that experimentally observed large fluctuations of MR versus σF 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 García et al. for MR of the magnetic nanocontacts
