This invention is directed to a method for purifying argon from an impure argon stream. If the oxygen concentration in the impure argon is less than about 10 mole percent of oxygen, the invention is proceeded in the sequential steps of a) removing chlorine from the impure argon stream; b) adding hydrogen to the impure argon stream; c) removing carbon dioxide and water from the impure argon stream; d) removing hydrogen from the impure argon stream; and e) removing nitrogen from the impure argon stream to form a purified argon stream. If the oxygen concentration in the impure argon is greater than about 10 mole percent of oxygen, the method comprises the sequential steps of a) removing chlorine from the impure argon stream; b) removing carbon dioxide and water from the impure argon stream; c) removing nitrogen and oxygen from the impure argon stream; d) adding hydrogen to the impure argon stream; e) removing water from the impure argon stream; f) removing hydrogen from the impure argon stream; and g) removing nitrogen from the impure argon stream to form a purified stream.