A method of enhancing the oxygen carrying ability of blood, comprising:injecting into the circulatory system of a subject, a modified hemoglobin bonded to the terminal groups of poly(alkylene oxide) through the amino groups in said hemoglobin by a linking group of the structure: --CH2 --O--(CH2)n --CONH--Hb, wherein Hb represents said hemoglobin and n is a positive integer.