To provide a method for producing the subject compound useful as a bleaching agent, and capable of avoiding the use of an acid chloride, reducing salt formation associated with the use of the acid chloride and dispensing with the isolation of the reaction intermediate, through ring opening of an N- acyllactam.

(A) The ring of an N-acyllactam is opened (preferably, an aqueous sulfuric acid of 50-96 wt.% in concentration is used in an amount of 3-7 times the component A by weight, and excess water of 1-10 times the carbonyl group of the component A by mol is further used) to obtain (B) the corresponding amidocarboxylic acid; and then the component B is oxidized (preferably, using a hydrogen peroxide aqueous solution of 25-85 wt.% in concentration under an oxidation temperature of 20-35°C). Further, the reaction is preferably carried out without isolating the component B; and the objective compound is expressed by formula I (R1 is a 1-20C alkyl, a 2-20C alkenyl or the like; R2 is a 1-20 alkylene, a 2-20 alkenylene or the like) or formula II (R3 and R4 are same as R2), e.g. N,N'-di-(4-percarboxybenzoyl-1,4-butanediamine.