To provide a secondary battery capable of maintaining the cyclic operating performance of battery at a low temperature and lessening the irreversibly operating capacity in the first cycle.

A carbonate additive for an electrolytic solution has a linear or cyclic form, has O-X and O-Y bond on both sides of carbonyl radical, and has a general structural formula of X-O-CO-O-Y. At least either of the O-X bond and O-Y bond has a dissociation energy smaller than about 80 kcal/mol, and X and Y are either identical or different, X being NR1R2 or CR3R4R5 and Y being NR'1R'2 or CR'3R'4R'5, wherein R1, R2, R3, R4, R5 and R'1, R'2, R'3, R'4, R'5 are either identical or different, where at least R3 is an unsaturated substitutional radical in case X is CR3R4R5 while Y is CR'3R'4R'5 so that an alkali metal is formed and thereby the intended battery is accomplished including a negative electrode to make intercalation into the alkali metal, a positive electrode containing an electrode active material to make intercalation into the alkali metal, non-aqueous electrolytic solution to activate the negative and positive electrodes, and additives.