Process for continuously preparing unsaturated carboxylic anhydrides of the general formula I R—C(O)—O—C(O)—R  (I) in which R is an unsaturated organic radical having 2 to 12 carbon atoms by transanhydridization of an aliphatic carboxylic anhydride with a carboxylic acid of the general formula II R—COOH  (II) in which R is as defined above in a rectification column having an upper, middle and lower region, characterized in that f) an inert boiling oil is initially charged in the bottom of the column, g) the reactants are fed into a reaction region in stoichiometric ratios, h) the carboxylic acid formed as the by-product is withdrawn at the top of the column, i) the unconverted reactants are recycled into the reaction region and j) the product of the formula I is obtained via a side draw, preferably between the middle and lower column region.