The invention is directed to a method for recovering carboyxlic acid from an magnesium carboxylate containing aqueous mixture comprising, comprising the steps of - contacting the aqueous mixture with an acidic ion exchanger, thereby forming a carboxylic acid mixture and ion exchanger loaded with magnesium ions; and - contacting the ion exchanger loaded with magnesium ions with a hydrochloric acid solution, thereby forming a magnesium chloride solution; and - thermally decomposing the magnesium chloride solution a temperature of at least 300 DEG C, thereby forming magnesium oxide (MgO) and hydrogen chloride (HC1).