Brine (an aqueous solution of alkali metal chlorine) which is electrolyzed according to the amalgamation process, generally contains small amounts of mercury. It has been found that these traces of mercury are entrained with the evaporated water in a considerable amount when applying evaporation cooling to the brine. In order to keep these losses as low as possible, a pH of from 7 to 9.0 and a redox potential more than 1391-6.66(pH)-5.94(pH).sup.2 but not more than 1100 mV (based on the potential of the hydrogen electrode) is adjusted by adding chlorine or alkali metal hypochlorite and optionally alkali metal hydroxide to the brine.