NOVELTY - A spinel-type lithium-manganese complex oxide has Brunauer-Emmett-and-Teller specific surface area of 1-2 m2/g and tap density of 0.5-1 g/cm3. The particle diameter (d10) of lithium-manganese complex oxide with 10 volume% accumulation in particle size distribution is 2-5 mu m. The particle diameter (d50) of lithium-manganese complex oxide with 50 volume% accumulation in particle size distribution is 6-9 mu m. The particle diameter (d90) of lithium-manganese complex oxide with 90 volume% accumulation in particle size distribution is 12-15 mu m.    USE - Spinel-type lithium-manganese complex oxide for positive electrode of lithium ion battery (both claimed) used as power supply for notebook personal computer, video camera, digital camera, mobile telephone and electric vehicles.    ADVANTAGE - The lithium-manganese complex oxide has favorable applicability with respect to collector. The battery comprising positive electrode containing lithium-manganese complex oxide has excellent high-temperature cycle characteristics and high capacity.    DETAILED DESCRIPTION - A spinel-type lithium-manganese complex oxide has Brunauer-Emmett-and-Teller specific surface area of 1-2 m2/g and tap density of 0.5-1 g/cm3. The particle diameter (d10) of lithium-manganese complex oxide with 10 volume% accumulation in particle size distribution is 2-5 mu m. The particle diameter (d50) of lithium-manganese complex oxide with 50 volume% accumulation in particle size distribution is 6-9 mu m. The particle diameter (d90) of lithium-manganese complex oxide with 90 volume% accumulation in particle size distribution is 12-15 mu m. The lithium-manganese complex oxide has compositional formula: Li1+xMn2-yMyO4.    M=aluminum magnesium, silicon, calcium, titanium, copper, barium, tungsten or lead;    x=-0.1 to 0.2;    y=0.06-0.3;and    (1+x)/2=0.51-0.58.    An INDEPENDENT CLAIM is included for manufacture of spinel-type lithium-manganese complex oxide, which involves heating and oxidizing mixture containing lithium, manganese and aluminum magnesium, silicon, calcium, titanium, copper, barium, tungsten or lead at 350-700 degrees C for 3-9 hours in 250 degrees C/hour in a continuous furnace, oxidizing at 800-1000 degrees C for 1-5 hour, and cooling at 300 degrees C/hour.