The process for the brightening of continuously produced sodium hydrogensulfate obtained in the reaction of sodium chloride and concentrated sulfuric acid in molten sodium hydrogensulfate in a circulation reactor, wherein evolved hydrogen chloride and heating gases generated by an immersion burner are withdrawn at various sites and seed crystals are added for a faster conversion of initially formed metastable phases, is that from 0.01 to 0.05% by weight of aluminium oxide and/or from 0.5 to 1.5% by weight of magnesium oxide and/or magnesium sulfate and, optionally, additionally calcium sulfate are added as seed crystals.