To obtain the subject hydroxamate that is useful for producing an antimicrobial agent by reaction of a specific amino acid with [(2,2,2- trichloroethoxy)methoxy]amine, ring closure of the product followed by treatment of the ring compound with zinc dust.

(A) A compound of formula I (A is an amino-protecting group; R1 and R2 are each H or an alkyl) is allowed to react with (B) [(2,2,2- trichlorethoxy)methoxy]amine and the resultant product is treated with, for example, triphenyl phosphine and diethyl azodicarboxylate to effect ring closure followed by treatment of the cyclic compound with zinc dust to eliminate 2,2,2- trichloroethoxymethyl group in the compound of formula II to give the objective compound of formula III.