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The behavior of the magnetoresistance (MR) effect in a ferromagnetic Ni nanocontact is investigated in the regime of conductance quantization (1/12900 Ω-1). The giant MR effect is observed in the case that the nanocontact with quantized conductance is fabricated. We sometimes observe that the conductance discretely changes by the quantization unit of e2/h and that the quantized conductance is switched by the application of magnetic field. There exists a close relationship between nanocontact MR and quantized conductance.