A method of purifying the raw brine used in the elecrolysis of the aqueous NaCl or KCl solution by removing the Mg and Ca ions from said brine, which comprises contacting said brine with a member selected from the group consisting of(a) the chelate-forming water-insoluble resins capable of forming an intramolecular complex with the Mg and Ca ions, said resins being selected from the class consisting of the styrene-butadiene copolymer resins containing the group >N--CH.sub.2 COOH, the epichlorohydrin polymer resins containing the group >N--CH.sub.2 COOH, the N-phenyl glycine-glycidyl methacrylate copolymer resins containing the group >N--CH.sub.2 COCH and the styrene-divinylbenzene copolymer resins containing the group >N--CH.sub.2 COOH; and(b) the water-insoluble adsorbent solids adsorptively supporting a chelate-forming compound selected from the group consisting of the aminoacetic acids containing at least one >N--CH.sub.2 COOH in their molecular structure and the oligomers and the alkali metal salts thereof.