Intermediates of formula (Ia) or (Ib) are provided: wherein R 11 and R 21 represents a hydrogen atom or an amino-protecting group, and R 16 represents an amino-protecting group, useful for the production of quinolone synthetic antibacterial agent of formula (I) wherein substituents R 6 and R 7 taken together with the carbon atoms to which they are bonded form a cyclic structure which may contain an oxygen atom as a ring constituent atom, the cyclic structure forming a 5-4, 5-5, or 5-6 fused bicyclic pyrrolidinyl substituent, the substituent being bonded to a quinolone mother skeleton Q containing a pyridobenzoxazine structure:
