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PROBLEM TO BE SOLVED : To restrain the reduction in battery capacity and control the activity of a positive electrode surface to improve the cycle life by introducing a fluoride of rare earth element and/or an acid fluoride of rare earth element to a composite oxide containing lithium, transition metal and oxygen. SOLUTION : As the composite oxide containing lithium, transition metal and oxygen to be used for a positive electrode active material for nonaqueous secondary battery, any composition, if usable for a positive electrode of nonaqueous secondary battery, can be used without particular limitation. Examples of the composite oxide composition for introducing a fluoride of rare earth element and/or an acid fluoride of rare earth element include LiCoO2, LiNiO2 and a composition in which each site of LiCoO2 or LiNiO2 is partially substituted by other elements. The quantity of the fluoride of rare earth metal and/or the acid fluoride of rare earth element to be introduced to the composite oxide in the positive electrode active material is preferably set to 0.3-10 wt.% to the total quantity of the composite oxide.