A cation-exchange membrane for electrolyzing an aqueous solution of an alkali metal halide in the manufacture of an alkali hydroxide and a halogen. The membrane comprises one layer which occupies 5 to 30% of the total thickness of the membrane and has carboxylic acid groups; another layer which occupies 5 to 30% of the membrane thickness and has weakly acidic groups, the weakly acidic groups occupying 10 to 60% of the total exchange group capacity of the layer; and a further layer which has sulfonic acid groups occupying the middle portion of the membrane.