NOVELTY - Complex oxide is obtained from raw material comprising metal salt of lithium nitrate and water soluble elements. The complex oxide has composition comprising lithium oxide, metal (M) having trivalent oxidation state, preferably nickel, and metal (M') having tetravalent oxidation state, preferably manganese. The ratio of crystal plane diffraction intensity of 21 degrees and (003) plane of complex oxide is 0-0.06. The complex oxide has specified ratio of crystal plane diffraction intensity of (003) plane and (104) plane, and crystal plane diffraction intensity of (101) and (104) plane.    USE - Complex oxide used for nonaqueous secondary battery (claimed). Uses include but are not limited to mobile telephone, portable audio, personal computer, integrated circuit tag, hybrid vehicle, plug-in hybrid motor vehicle, electric vehicle and electrical storage system for residence.    ADVANTAGE - The complex oxide is manufactured by simple method, and provides nonaqueous battery having high capacity.    DETAILED DESCRIPTION - Complex oxide is obtained from raw material comprising metal salt of lithium nitrate and water soluble elements (M and M'). The complex oxide contains composition of formula: X(LiMO2)x (1-X)Li2M'O3. The ratio (I(21( degrees ))/I(003)) of crystal plane diffraction intensity of 21 degrees and (003) plane of complex oxide is 0-0.06, when I (21( degrees )) and crystal plane diffraction intensity of (003) plane are set to I(003) for diffraction peak intensity derived from super lattice of 21 degrees vicinity in X-ray-diffraction measurement. The ratio of crystal plane diffraction intensity of (003) plane and (104) plane is 2-5 and the ratio of crystal plane diffraction intensity of (101) and (104) plane is 0.4-0.5, when the crystal plane diffraction intensity of surface is set to I(003), I(101) and I(104).    x=0-1;    M=metal having trivalent oxidation state, preferably nickel;and    M'=metal having tetravalent oxidation state, preferably manganese.    INDEPENDENT CLAIMS are included for the following:    (1) manufacture of complex oxide, which involves dissolving the raw material and drying the dissolved raw material mixture at 100-300 degrees C; and    (2) nonaqueous secondary battery, which contains complex oxide as positive electrode active material.