In a process for producing an alkali metal hydroxide which comprises electrolysis of an aqueous solution of an alkali metal chloride in an electrolytic cell having an anode compartment and a cathode compartment which are partitioned by a fluorinated cation exchange membrane, the improvement which comprises a fluorinated cation exchange membrane made of a fluorinated copolymer having carboxylic acid groups as the ion exchange group and having an ion exchange capacity of 0.5 to 2.0 meq/g dry polymer and a concentration of carboxylic acid groups of 8 to 30 meq/g water absorbed by the membrane when contacted with an aqueous solution of the alkali metal hydroxide having about the same concentration of alkali metal hydroxide as that of catholyte during said electrolysis.