NOVELTY - Positive-electrode active material particle powder having spinel structure contains composition containing lithium-manganese-nickel-metal oxide. When indexing is carried out by Fd-3m in X-ray diffraction of the positive-electrode active material particle powder, the ratio (I(311)/I(111)) of intensity at planes (311) and (111), is 35-43%. When half-value width for each peak position at angle (2 theta ) of 10-90 degrees , the inclination of straight line obtained by the least squares method in graph with sin( theta ) as horizontal axis and Bcos( theta ) as vertical axis, is 3x 10-4-20x 10-4.    USE - Positive-electrode active material particle powder for nonaqueous electrolyte secondary battery (claimed) used as power supply for audio-video equipment, personal computer, electric vehicle and hybrid vehicle.    ADVANTAGE - The nonaqueous electrolyte secondary battery using the positive-electrode active material particle powder has excellent cycle characteristics and high discharge capacity.    DETAILED DESCRIPTION - Positive-electrode active material particle powder having spinel structure contains composition containing lithium-manganese-nickel-metal oxide (Li1+xMn2-y-zNiyMzO4). When indexing is carried out by Fd-3m in X-ray diffraction of the positive-electrode active material particle powder, the ratio (I(311)/I(111)) of intensity at planes (311) and (111), is 35-43%. When half-value width for each peak position at angle (2 theta ) of 10-90 degrees , the inclination of straight line obtained by the least squares method in graph with sin( theta ) as horizontal axis and Bcos( theta ) as vertical axis, is 3x 10-4-20x 10-4.    x=-0.05-0.15;    y=0.4-0.6;    z=0-0.2;and    M=Mg, Al, Si, Ca, Ti, Co, Zn, Sb, Ba, W, and Bi.    INDEPENDENT CLAIMS are included for the following:    (1) manufacture of positive electrode active material particle powder, which involves mixing manganese and nickel-containing compound and lithium compound, baking at 680-1050 degrees C under oxidative atmosphere, and baking at 500-700 degrees C;    (2) nonaqueous electrode electrolyte battery;    (3) manganese-nickel complex oxide particle powder, which has average particle diameter of 1-8 mu m;    (4) manufacture of manganese-nickel complex oxide particle powder, which involves neutralizing manganese salt aqueous solution using alkali solution, oxidizing at 60-100 degrees C, obtaining tri-manganese tetraoxide core particles, adding manganese raw material and nickel raw material to the obtained reaction solution, obtaining manganese-nickel complex compound by second order reaction and baking at 900-1100 degrees C under oxidative atmosphere; and    (5) manufacture of positive electrode active material particle powder, which involves mixing manganese-nickel complex oxide powder and lithium compound, baking at 680-1050 degrees C under oxidative atmosphere, and baking at 500-700 degrees C.