A process for removing sulfur dioxide from flue gases where calcium sulfate and magnesium hydroxide are produced, with the magnesium hydroxide separated in an impure state and purified by addition of water thereto to dissolve contaminant calcium sulfate. The calcium sulfate preferentially dissolves to form an aqueous solution and purified magnesium hydroxide is separated therefrom. At least a portion of the resultant aqueous solution of calcium sulfate is returned to the wet scrubbing system as make-up water to replenish water lost from the aqueous medium during scrubbing of the flue gases.