NOVELTY - A positive-electrode active material comprises a lithium-nickel-manganese-metal complex oxide, where the metal is cobalt, vanadium, molybdenum, titanium, aluminum, magnesium and/or iron. The half value width of the X-ray-diffraction peak at 2( theta ) of 18.6 plus minus 1 degrees measured by powder X-ray diffraction by CuK alpha are 0.12-0.17 degrees , and that at 2( theta ) of 44.4 plus minus 1 degrees is 0.18-0.22 degrees . The active material has a BET specific surface area of 2 m2/g or more.    USE - Active material is used for positive electrodes of lithium ion secondary batteries (all claimed). Uses include but are not limited to electric vehicles, natural energy electric power generation, elevators, hybrid type electric vehicles, power supplies for business use or domestic use, information-technology equipment, domestic electrical appliances, and electric tools.    ADVANTAGE - The positive-electrode active material provides lithium ion secondary batteries having low direct-current internal resistance and high discharge capacity.    DETAILED DESCRIPTION - A positive-electrode active material comprises a lithium-nickel-manganese-metal complex oxide of formula: Li1+xNiyMnzMwO2, where M is cobalt, vanadium, molybdenum, titanium, aluminum, magnesium and/or iron, x is 0.1-0.25, y is 0.25-0.5, z is 0.3-0.55, w is 0-0.1, and x+y+z+w is 1. The half value width of the X-ray-diffraction peak at 2( theta ) of 18.6 plus minus 1 degrees measured by powder X-ray diffraction by CuK alpha are 0.12-0.17 degrees , and that at 2( theta ) of 44.4 plus minus 1 degrees is 0.18-0.22 degrees . The active material has a BET specific surface area of 2 m2/g or more. INDEPENDENT CLAIMS are included for the following:    (1) positive electrode (2);    (2) lithium ion secondary battery (1); and    (3) manufacture of positive-electrode active material.    DESCRIPTION OF DRAWING(S) - The drawing shows a cross-sectional schematic view of the lithium ion secondary battery.    Lithium ion secondary battery (1)    Positive electrode (2)    Negative electrode (3)    Separator (4)    Battery can (5)