NOVELTY - A positive electrode active material comprises hexagonal lithium-nickel-cobalt-manganese-metal oxide complex (I). The complex has layered structure. The ratio of integral width of diffraction peak by (003) plane in Miller index and integral width of diffraction peak by (104) plane of the complex is 1.38 or more, measured in powder X-ray diffraction using copper-K alpha line.    USE - Positive electrode active material is used for nonaqueous electrolyte secondary battery (claimed) used for electric vehicle, power tool, hybrid vehicle and portable electronic device e.g. mobile telephone and notebook computer.    ADVANTAGE - The positive electrode active material is safe and has excellent thermal stability. The nonaqueous electrolyte secondary battery having excellent capacity and output characteristics even under extremely-low-temperature environment, is obtained using the positive electrode active material, by economical and simple process.    DETAILED DESCRIPTION - A positive electrode active material comprises hexagonal lithium-nickel-cobalt-manganese-metal oxide complex of formula: Li1+aNixCoyMnzMtO2 (I). The complex has layered structure. The ratio of integral width of diffraction peak by (003) plane in Miller index and integral width of diffraction peak by (104) plane of the complex is 1.38 or more, measured in powder X-ray diffraction using copper-K alpha line.    a=(-0.05)-0.20;    x+y+z+t=1;    x=0.30-0.70;    y,z=0.10-0.40;    t=0-0.01;and    M=Ca, Mg, Al, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta or W.    INDEPENDENT CLAIMS are included for the following:    (1) manufacture of positive electrode active material, which involves mixing nickel-cobalt-manganese composite hydroxide particles of formula: NixCoyMnzMt(OH)2+b, and lithium compound, such that ratio of number of lithium atoms to the sum total of the number of atoms of metallic elements other than lithium is 1:0.95-1.20, obtaining lithium mixture, increasing the temperature of the mixture to 30-800 degrees C in rate of 4-10 degrees C/minute under oxidative atmosphere, calcining at 800-1000 degrees C for less than 5 hours and baking for 3-7 hours; and    (2) nonaqueous electrolyte secondary battery, which is equipped with a positive electrode containing positive electrode active material, a negative electrode, a separator, and a nonaqueous electrolyte.    b=0-0.5.    N.B: b is defined in the disclosure, but not in the claims.