A process is, herein, disclosed for electrolysis or pure water in an electrolytic cell which is divided into an anode compartment and a cathode compartment by a cation exchange membrane and in which pure water is supplied to the anode compartment for electrolysis to generate oxygen in the anode compartment and hydrogen in the cathode compartment, said cation exchange membrane being produced by grafting a fluorovinyl sulfonic acid monomer onto a membranous polymeric substrate having a monomer unit of the formula: ##STR1## (wherein X is hydrogen, fluorine or CH.sub.3 ; and Y is hydrogen or fluorine), said cation exchange membrane being used in close contact with an anode and a cathode.