NOVELTY - Positive electrode active material contains lithium transition-metal complex oxide of layered structure. Inclination of primary regression of a straight line passing through the origin, is 1.5-2.66. Straight line is drawn using the cubic roots of light-emission voltage resulting from transition metal of complex oxide as X-coordinates, and that resulting from lithium of complex oxide particle as Y-coordinates.    USE - For non-aqueous-electrolyte secondary battery (claimed), such as rechargeable lithium-ion batteries, used for notebook personal computers, pen input personal computers, pocket personal computers, note-type word processors, pocket word processors, electronic book players, mobile telephones, cordless phone mobile units, electronic notebooks, calculators, liquid crystal televisions, electric shavers, power tools, electronic translating machines, vehicle telephones, portable printers, transceivers, pagers, hand-held terminals, portable copiers, audio input devices, memory cards, backup power supplies, tape recorders, radios, headphone stereo cassette tape recorders, hand-held cleaners, portable CD players, navigation systems, light equipment devices, air conditioners, water heaters, refrigerators, ovens, dishwashing devices, washing machines, driers, game machine devices, toys, load conditioners, medical equipment, motor vehicles, electric vehicles, golf carts, digital cameras, electrically-driven carts, and electric power storage systems.    ADVANTAGE - The positive electrode active material provides non-aqueous-electrolyte secondary batteries having excellent battery property, overcharge property, and safety even in severe conditions. The positive electrode active material improves voltage drop without impairing improvement in cycle charging-and-discharging property, heat stability, and output characteristics.    DETAILED DESCRIPTION - The positive electrode active material contains a lithium transition-metal complex oxide of layered structure. The inclination of the primary regression of a straight line passing through the origin, is 1.5-2.66. The straight line is drawn using the cubic roots of the light-emission voltage resulting from the transition metal of the complex oxide particle as X-coordinates, and the cubic roots of the light-emission voltage resulting from lithium of the complex oxide particle as Y-coordinates.    An INDEPENDENT CLAIM is included for non-aqueous-electrolyte secondary battery.    DESCRIPTION OF DRAWING(S) - The figure shows a sectional drawing of a cylindrical cell.    Cathode (11)    Collector (12)    Positive electrode (13)    Separator (14)    Cylindrical cell (20)