TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The electrolyte solution further contains lithium hexafluorophosphate. The electrolyte solution contains lithium imide electrolyte (0.005-2 mol/l). The lithium imide electrolyte(s) includes cyclic lithium imide salt of formula (1). The ratio of nickel in the lithium-transition metal composite oxide is 6 atomic% or more with respect to 100 atomic% of transition metal.x=1-8. EXAMPLE - Lithium-nickel-cobalt-aluminate (LiNi0.8Co0.2AlO2) powder (in mass parts) (50) having average particle diameter of 20 microns, lithium-nickel-cobalt-manganese oxide (LiNi0.34Co0.33Mn0.33O2) powder (20) having average particle diameter of 10 microns and lithium-cobalt oxide (LiCoO2) powder (30) having average particle diameter of 10 microns were mixed to obtain a mixture. The obtained mixture (91), polyvinylidene fluoride (3) and KS-15 (RTM: artificial graphite) (6) were mixed and dispersed to N-methyl-2-pyrrolidone, to obtain anode-mix slurry. The slurry was then coated over anode collector, dried and molded to obtain anode. The graphite powder (94), vapor grown carbon fiber (1) and polyvinylidene fluoride (5) were dispersed in N-methyl-2-pyrrolidone, to obtain cathode slurry. The slurry was then coated over cathode collector, dried and molded to obtain cathode. Lithium hexafluoride (0.5 mol/l) and lithium imide salt of formula (2) (0.5 mol/l) were added to the mixed solvent of ethylene carbonate (30%), propylene carbonate (5%), vinylene carbonate (1%), ethyl methyl carbonate (4%) and dimethyl carbonate (60%), to obtain electrolyte solution. The obtained anode, cathode, polyethylene separator having thickness of 16 microns were assembled in a nickel plated battery-can and electrolyte solution was injected, to obtain cylindrical secondary battery having diameter of 18 mm and height of 65 mm. The obtained battery was free from defects and had excellent cycle characteristics at 50degrees C with discharge capacitance maintenance factor of 83%.