NOVELTY - A deposit is formed using mixed aqueous solution containing titanium compound and/or iron compound, and manganese compound. A deposit soluble lithium compound is obtained by performing oxidation and aging treatment of deposit by blowing air into the reaction solution. The resulting deposit is subjected to hydrothermal treatment in alkaline conditions with soluble lithium compound, in order to obtain positive electrode material. The positive electrode material comprises composition (I), and has lithium manganese oxide-type crystal phase of monoclinic layered rock-salt structure.    USE - Manufacture of positive electrode material used for lithium ion secondary battery. Uses include but are not limited to electric vehicle, electric power load-leveling system, mobile telephone and notebook personal computer.    ADVANTAGE - The method enables economical manufacture of positive electrode active material having excellent equivalent/discharge capacity of 200 mAh/g or more, weight energy density of 600 mWh/g or more, and average discharge voltage of 3 V or more in prolonged charging/discharging cycle. The battery consisting of the positive electrode material has charge-and-discharge characteristics.    DETAILED DESCRIPTION - A deposit is formed using mixed aqueous solution containing compound chosen from titanium compound and iron compound, and manganese compound as alkaline. A deposit soluble lithium compound is obtained by performing oxidation and aging treatment of deposit by blowing air into the reaction solution. The resulting deposit is subjected to hydrothermal treatment in alkaline conditions with soluble lithium compound, in order to obtain positive electrode material. The positive electrode material comprises composition of formula: Li1+x(Mn1-m-nFemTin)1-xO2, and has lithium manganese oxide-type crystal phase of monoclinic layered rock-salt structure. The average valence of manganese element made of lithium-manganese-based composite oxide is 3.9 or less.    x=0-1/3;    m,n=0-0.53;and    m+n=0.53 or less.