An electrolysis of an aqueous solution of potassium chloride is carried out by employing a fluorinated cation exchange membrane having an ion-exchange capacity of 0.8 to 2.0 meq/g dry polymer and having carboxylic acid groups as functional groups and maintaining a concentration of an aqueous solution of potassium hydroxide in a cathode compartment in a range of 20 to 45 wt. % and maintaining a calcium concentration in the aqueous solution of potassium chloride to lower than 0.05 mg/liter.The purification of the aqueous solution of potassium chloride to reduce the calcium concentration is carried out in a system comprising a chelate ion-exchange substance.