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PROBLEM TO BE SOLVED : To provide a positive active material for a lithium secondary battery, having large volume capacity density, high safety, excellent uniform coatability, and excellent charging/discharging cycle durability and low temperature characteristics. SOLUTION : This method is for manufacturing a lithium-cobalt compound oxide expressed by a general expression, LipCoxMyOzFaby baking a mixture including a cobalt source and a lithium source in an oxygen-containing atmosphere (where, M is a transition metal element other than Co, or an alkaline earth metal element. 0.9≤p≤1.1, 0.980≤x≤1.000, 0≤y≤0.02, 1.9≤z≤2.1, x+y=1, and 0≤a≤0.02). As the cobalt source, a mixture is used including cobalt oxyhydroxide, wherein the average grain size of secondary grains is 7 to 20μm into which primary grains are aggregated, and substantially spherical cobalt hydroxide or tricobalt tetroxide, wherein the average grain size of secondary grains is 8 to 20μm into which primary grains are aggregated, at a cobalt atom ratio of 5 : 1 to 1 : 5, and baked at 700 to 1, 050°C. COPYRIGHT : (C)2004, JPO