A marked difference in spin relaxation behavior due to hemoglobin magnetism was found for positive muons (μ(+)) in deoxyhemoglobin in comparison with that observed in oxyhemoglobin in aqueous solution at room temperature under zero and external longitudinal magnetic fields upto 0.4 Tesla. At the same time, small but significant unique relaxation pattern was observed in nonmagnetic oxyhemoglobin. Combined with our previous measurements on hemoglobin in human blood, application of this type of measurement to the studies of the level of oxygenation in various regions of the human brain is suggested.