NOVELTY - A positive-electrode active material consists of a coating layer containing microparticles of lithium-cobalt complex oxide and lithium-manganese complex oxide formed on the surface of primary particles of lithium-metal complex oxide. The sum total atom number of cobalt and manganese in the coating layer is 0.7-0.9 atomic% with respect to the sum total atom number of metal except lithium contained in the primary particles. The molar ratio of manganese with respect to sum total of cobalt and manganese is 0.05-0.2.    USE - Positive-electrode active material is used for non-aqueous electrolyte secondary batteries (claimed) of mobile telephones, notebook computers, hybrid vehicles, and electric vehicles driven with electrical energy, gasoline engines, or diesel engines.    ADVANTAGE - The positive-electrode active material provides non-aqueous electrolyte secondary batteries having excellent charging-and-discharging characteristics, heat stability, economical efficiency (as expensive protective circuit is simplified), and safety.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) manufacture of positive-electrode active material, which involves obtaining a slurry by mixing and stirring a powder consisting of lithium-metal complex oxide with water, add-stirring an aqueous solution obtaining by dissolving a cobalt salt and a manganese salt with in slurry, adhering microparticles comprising cobalt and manganese compounds to the surface of primary particles consisting of lithium-metal complex oxide to form a coating layer, and heat-processing the primary particles with coating layer at 300-700 degrees C; and    (2) non-aqueous electrolyte secondary battery having an initial-stage discharge capacity of 195 mAh/g or more.    DESCRIPTION OF DRAWING(S) - The drawing shows a perspective view and a sectional view of a coin battery used for evaluation of initial-stage capacity of the positive-electrode active material.    Lithium metal negative electrode (1)    Separator (2)    Positive electrode (3)    Gasket (4)    Collector (7)