NOVELTY - A raw material mixture containing lithium compound powder and powder containing nickel and cobalt, powder containing nickel, cobalt, and manganese, or powder containing nickel, cobalt, manganese, and element (M) is temporarily-baked at a temperature of 300-600 degrees C, to prepare a temporarily-baked powder. A solution of cobalt compound is sprayed on the temporarily-baked powder, to prepare a cobalt compound addition powder. A lithium-containing complex oxide powder is prepared by baking the cobalt compound addition powder, to obtain the positive electrode active material.    USE - Manufacture of positive electrode active material used for manufacture of positive electrode used for manufacture of lithium-ion secondary battery (all claimed) used in vehicles.    ADVANTAGE - The method enables the manufacture of positive electrode active material with high capacitance and density, by simple process, and provides the lithium-ion secondary battery with excellent charging or discharging cyclic characteristics, and suppresses the raising of impedance in the positive electrode active material.    DETAILED DESCRIPTION - A raw material mixture containing lithium compound powder and powder containing nickel and cobalt, powder containing nickel, cobalt, and manganese, or powder containing nickel, cobalt, manganese, and element (M) is temporarily-baked at a temperature of 300-600 degrees C, to prepare a temporarily-baked powder. A solution of cobalt compound is sprayed on the temporarily-baked powder, to prepare a cobalt compound addition powder. A lithium-containing complex oxide powder is prepared by baking the cobalt compound addition powder at 720-1100 degrees C, to obtain the positive electrode active material. The element (M) contains group-2 elements or transition metals chosen from nickel, cobalt, manganese, aluminum, and tin. The atomic ratio of lithium with respect to sum of total amount of nickel, cobalt, manganese, and element (M) contained in the raw material mixture is 0.95-1.3. INDEPENDENT CLAIMS are included for the following:    (1) manufacture of positive electrode, which involves preparing slurry by mixing positive electrode active material, electroconductive agent, binder, and solvent, coating the prepared slurry on a metal foil, and removing the solvent by heating; and    (2) manufacture of lithium-ion secondary battery, which involves forming an assembly by laminating a separator and a negative electrode on the positive electrode, injecting an electrolyte solution, and accommodating the formed assembly in a battery case.