The invention is directed to a method for recovering carboyxlic acid from an magnesium carboxylate containing aqueous mixture, including the steps of: contacting the aqueous mixture with an acidic ion exchanger, thereby forming a carboxylic acid mixture and an ion exchanger loaded with magnesium ions; 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 at a temperature of at least 300° C., thereby forming magnesium oxide (MgO) and hydrogen chloride (HCl).