a method for preventing the accumulation of an alkali sulfate produced as a by - product in the system for removing sulfur dioxide from exhaust gases containing sulfur dioxide is disclosed , the system comprising bringing the exhaust gas into contact with an aqueous solution containing an alkali sulfite to absorb sulfur dioxide into the solution and to convert the absorbed sulfur dioxide to an acidic alkali sulfite , adding calcium carbonate for the double decomposition of acidic alkali sulfite into the thus obtained aqueous solution containing the acidic sulfite and after removing the precipitated calcium sulfite and accompanying calcium sulfate by filtration , circulating the filtrate as aqueous solution for absorption of sulfur dioxide in the above - mentioned exhaust gas , the method being characterized in that the double decomposition is carried out in two stages by adding calcium carbonate of different particle size , respectively and the filtration is carried out , preferably , in an atmosphere of carbon dioxide to prevent the oxidation of sulfite by oxygen in air .