NOVELTY - A positive electrode active material contains a boron compound and hexagonal type lithium-nickel-cobalt-manganese complex oxide (I) having layered structure. The complex oxide comprises secondary particles formed by aggregation of primary particles. The boron compound containing lithium exists on a portion of the primary-particle surface.    USE - Positive electrode active material used for positive electrode of non-aqueous electrolyte secondary battery (claimed). Uses include but are not limited to mobile telephone, notebook computer, power tool, hybrid vehicle and electric vehicle.    ADVANTAGE - The positive electrode active material exhibits low resistance and provides non-aqueous secondary battery having excellent output characteristics even in extensive temperature environment, and high capacity.    DETAILED DESCRIPTION - A positive electrode active material contains a boron compound and hexagonal type lithium-nickel-cobalt-manganese complex oxide having layered structure. The complex oxide is given by the formula (I): Li1+sNixCoyMnzMotMwO2. The complex oxide comprises secondary particles formed by aggregation of primary particles. The boron compound containing lithium exists on a portion of the primary-particle surface.    s=-0.05-0.20;    x+y+z+t+w=1;    x=0.1-0.7;    y,z=0.1-0.5;    t=0.0003-0.05;    w=0-0.05;and    M=Ca, Mg, Al, Ti, V, Cr, Zr, Nb, Hf and/or Ta.    INDEPENDENT CLAIMS are included for the following:    (1) manufacture of positive electrode active material, which involves mixing a lithium compound with particles of nickel-cobalt-manganese composite hydroxide of formula (II): NixCoyMnzMotMw(OH)2+a, where a is 0-0.5, to obtain a lithium mixture such that the ratio number of atoms of lithium with respect to total of number of atoms of metallic elements excluding lithium is 0.95-1.20, baking the obtained lithium mixture at calcination temperature of 800-1000 degrees C for 5-20 hours in oxygen atmosphere to obtain lithium nickel cobalt manganese complex oxide particles, mixing a boron raw material with the lithium nickel cobalt manganese complex oxide particles to obtain a boron mixture, and heat-processing the boron mixture at 300-580 degrees C in oxygen atmosphere; and    (2) non-aqueous electrolyte secondary battery, which has a positive electrode using the positive electrode active material, negative electrode, separator and non-aqueous electrolyte.