TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The layered lithium transition metal composite oxide comprises transition metal, 0.005-0.8 mol.% different element, and greater than or equal to 10 mass% positive electrode active material. Preferred Components: The layered lithium-transition metal composite oxide is lithium-cobalt composite oxide, lithium-nickel composite oxide, lithium-cobalt nickel composite oxide, lithium manganese nickel composite oxide or lithium cobalt manganese nickel composite oxide; and is in the form of spherical or elliptical particles. The non-aqueous solvent contains a cyclic carbonate. The negative electrode is graphite having non-crystallized surface.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The tert. carboxylic ester is methyl trimethylacetate and/or ethyl trimethyl acetate. EXAMPLE - An electrode assembly was prepared by winding up positive and negative electrodes with separator interposed between them. The positive electrode was prepared by mixing (parts by mass) zirconium lithium-cobalt composite oxide (95), acetylene back (3), polyvinylidene fluoride (2) and N-methyl-2-pyrrolidone to prepared a slurry; applying the slurry to both sides of aluminum positive electrode current collector; and drying and rolling the obtained dry electrode plate. The negative electrode was prepared by mixing artificial graphite with polyvinylidene fluoride, N-methyl-2-pyrrolidone to prepared a slurry; applying the slurry to both sides of copper negative electrode current collector; and drying and rolling the dried electrode. A non-aqueous electrolyte was prepared by mixing methyl trimethyl acetate and ethylene carbonate at mass ratio of 70:30, and dissolving lithium hexafluorophosphate as electrolyte salt. The electrode assembly and non-aqueous electrolyte were housed in outer can, and the opening of the outer can was sealed with sealing plate to complete non-aqueous electrolyte secondary battery having a design capacity of 950 mAh.