NOVELTY - Manufacture of spinel-type lithium-manganese-nickel-based complex oxide (I) involves wet blending manganese source, nickel source and source (M), pulverizing, spray-drying obtained spraying raw material slurry, heat-processing spray-dried material having average particle diameter of 5-20 mu m, mixing heat-processed material containing microparticles (0.5 %mass or less) having particle size of 1 mu m or less, and lithium source, baking obtained baking raw material mixture, and then, anneal-treating baked product, to obtain spinel-type lithium-manganese-nickel-based complex oxide.    USE - Manufacture of spinel-type lithium-manganese-nickel-based complex oxide used for positive mix for lithium secondary battery (all claimed). Uses include but are not limited to notebook personal computer, laptop computer, pocket word processor, mobile telephone, cordless phone unit, portable compact disk player, radio, motor vehicle, electric vehicle and game machine device.    ADVANTAGE - The lithium secondary battery containing the spinel-type lithium-manganese-nickel-based complex oxide has excellent charging and discharging characteristics, and high coulomb efficiency, discharge capacity maintenance factor, and ratio of 5V discharge capacity region with respect to sum of 5V discharge capacity region and 4V discharge capacity region.    DETAILED DESCRIPTION - Manufacture of spinel-type lithium-manganese-nickel-based complex oxide of formula: LixNiyMnzMaO4-w (I) involves wet blending manganese source and nickel source, or manganese source, nickel source and source (M), pulverizing to obtain spraying raw material slurry containing solid content having average particle diameter of 1 mu m or less, spray-drying the spraying raw material slurry to obtain spray-dried material having average particle diameter of 5-20 mu m, heat-processing the spray-dried material, mixing heat-processed material containing microparticles (0.5 %mass or less) having particle size of 1 mu m or less, and lithium source to obtain baking raw material mixture, baking the baking raw material mixture at 850-1100 degrees C to obtain baked product, and then, anneal-treating baked product at 500-700 degrees C, to obtain spinel-type lithium-manganese-nickel-based complex oxide (I).    x=more than 0.9 to less than 1.1;    y=0.4-0.6;    z=1.4-1.6;    a=0-0.2;    y+z+a=2;    w=0 to less than 2;and    M=element (excluding Ni and Mn) having atomic number of 11 or more.