A method of reducing the concentration of metal ions in pure water or ultrapure water and thereby obtaining pure water or ultrapure water. Such purified pure water or purified ultrapure water is used, for example, when washing semiconductor wafers, as a starting material of electrolytic ionic water, or for diluting washing water. A pair of carbon electrodes is disposed in an ultrapure water storage tank containing pure water or ultrapure water or in a purifying tank disposed in a line leading from an ultrapure water storage tank. A D.C. voltage is applied across the electrode pair. A carbon electrode material having a large specific surface area is chosen, and an electrode structure with which there is little detachment of carbon fragments is used. After the carbon electrode is molded, a carbon layer is formed on the surface of the molding by dipping the molding in an amorphous carbon bath. Because the carbon layer penetrates into the pores in the molding surface, the bonds between the carbon elements are strengthened, preventing carbon fragments from detaching. Because the electrode surfaces may be covered with filters, even if carbon fragments do detach, they are caught by the filters, preventing particles from entering the purified pure water or purified ultrapure water.