TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Compound: The nickel-containing lithium composite metal oxide is of formula LiNixMyLzO2.M=Co and/or Mn;L=Al, Mg, Ca, Si, and/or Ti;x=0.3-0.9;y=0.1-05;andz=0.005-0.1. EXAMPLE - A lithium nickel composite oxide (LiNi0.8Cu0.15Al0.05O2) was used as the active material. A positive electrode material mixture paste was applied onto both surfaces of a 15 microns thick current collector made of aluminum foil, which was then dried and rolled to form positive electrode material mixture layers integrally with the current collector. The resultant current collector was then cut providing a positive electrode. The total thickness of the aluminum foil and the positive electrode material mixture layers formed on both surfaces of the aluminum foil was 159 microns. The positive electrode material mixture layers had a porosity of 20%. A negative electrode material mixture paste was prepared by mixing 100 pbw of spherical natural graphite powder with 1 pbw of BM-400B(RTM: core-shell rubber particles containing an acrylonitrile group in the core and having a styrene group incorporated in the shell), 1 pbw of carboxymethyl cellulose, and water. The negative electrode material mixture paste was then applied onto both surfaces of a 10 microns thick current collector made of copper foil, which was then dried and rolled to form negative electrode material mixture layers integrally with the current collector. The resultant current collector was then cut producing negative electrode. The positive and negative electrodes were spirally wound with a 20 microns thick separator made of polypropylene interposed between them to form a columnar electrode group. The electrode group was then inserted into a cylindrical bottomed battery case, after which a non-aqueous electrolyte was injected into the battery case. The non-aqueous electrolyte was prepared by dissolving lithium phosphorus hexafluoride (LiPF6) in a non-aqueous solvent of ethylene carbonate (EC), dimethyl carbonate (DMC), and ethyl methyl carbonate (EMC) at a volume ratio of 10:20:70 at LiPF6 concentration of 1 mol/L. After injection, the opening of the battery case was sealed with a sealing plate and a gasket, providing a cylindrical lithium ion secondary battery (nominal capacity: 2800 mAh). The battery temperature in nail penetration test was 83. When the battery was subjected to cycle test at 25degreesC, the number of cycles was 510.