Synthesis of N-methyl-N-[(1S)-1-[(3R)-pyrrolidin-3-yl]ethyl]amine

N-Methyl-N-(1S)-1-(3R)-pyrrolidin-3-yl]ethyl]amine (1)(1) is a key intermediate in the preparation of premafloxacin (2), which was under development as an antibiotic for use against pathogens of veterinary importance. This paper describes the development of a practical, efficient, and stereoselective process for the preparation of 1 from isobutyl (3S)-3-methyl(1S)-1-phenylethyl]amino]butanoate (5c). The key steps in the synthetic sequence are an asymmetric Michael addition, which yields 5c, and a stereoselective alkylation, which yields (3S,4S)-3-allyl-1,4-dimethylazetidin-2-one (17).