PURPOSE: To manufacture lithium-containing manganese composite oxide excellent in a cycle characteristic by again mixing MnO2 of high purity obtained by acid treatment of LiMn2O4 with a lithium compound, followed by a heat treatment for synthesizing.

CONSTITUTION: Manganese dioxide on the market is subjected to a heat treatment, and is mixed with a predetermined quantity of lithium nitrate, followed by a heat treatment, thus obtaining LiMn2O4. The resultant LiMn2O4 is oxidized with sulfuric acid or the like, and then, the precipitate is recovered, thereby obtaining MnO2 of high purity. The resultant MnO2 is mixed with a predetermined quantity of lithium nitrate, followed by a heat treatment, thus composing LiMn2O4. Use of the resultant lithium containing manganese composite oxide of spinel crystal structure as a positive electrode active material can improve a cycle characteristic of a non-aqueous electrolyte secondary battery.