A novel process for preparing a prodrug acid, viz., 7-[(1 alpha , 6 alpha , 7 alpha )-6-(L-Ala-L-Ala-amino)-3-azabicyclo[3.1.0]hex-3-yl]-6-fluoro-1-(2,4-difluorophenyl)-1,4-dihydro-4-oxo-1,8-naphthyridine-3-carboxylic acid, in the form of a pharmaceutically acceptable acid addition salt, is disclosed, which involves (1) treating an N-protected 7-[(1 alpha , 5 alpha , 6 alpha )-6-amino-3-azabicyclo[3.1.0]hex-3-yl]-6-fluoro-1-(2,4-difluorophenyl)-1,4-dihydro-4-oxo-1,8-naphthyridine-3-carboxylic acid C1-C4 alkyl ester, wherein the nitrogen-protecting group is benzyloxycarbonyl, C1-C4 alkoxycarbonyl or C1-C4 alkanoyl, with a strongly-protic acid to selectively remove the N-protecting group; (2) then condensing the resulting free amino ester compound with an N-protected L-alanyl-L-alanine dipeptide compound, wherein the N-protecting group is as previously defined, in the presence of a standard dehydrating agent to form the corresponding N-protected prodrug ester compound as the desired condensation product; and (3) thereafter hydrolyzing the intermediate N-protected prodrug ester in the presence of a pharmaceutically-acceptable strong acid to convert said N-protected prodrug ester to the desired naphthyridinone L-Ala-L-Ala prodrug acid final product, in the form of the corresponding pharmaceutically acceptable acid addition salt, indicated above. The latter prodrug acid final product is especially useful in the form of the corresponding methanesulfonic acid addition salt, which serves as a water-soluble prodrug companion to a known antibacterial agent, viz., 7-[(1 alpha , 5 alpha , 6 alpha )-6-amino-3-azabicyclo[3.1.0]hex-3-yl]-6-fluoro-1-(2,4-difluorophenyl)-1,4-dihydro-4-oxo-1-naphthyridine-3-carboxylic acid.