TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: In step (a), at least one dopant consisting of magnesium, aluminum, calcium, titanium, vanadium, chromium, iron, copper, zinc, gallium, zirconium, molybdenum, tin, antimony, tungsten and bismuth is added in an amount of 0.01-2 mole%, based on the total moles of the first cathode active material, and the heat treatment is performed at 400-900 degrees C for 3-24 hours. In step (b), the molarity of the sodium hydroxide solution is 1.5-4 times higher than that of the mixed solution, and the pH is maintained at 11-12. The method further comprises washing, filtering and drying the coprecipitated hydroxide after the step (b). The water content of the dried coprecipitated hydroxide is adjusted to less than or equal to 10%. In step (c), the dopant is added in an amount of 0.01-2 mole%, based on the total moles of the second cathode active material and the heat treatment is performed at 400-900 degrees C for 3-24 hours. In step (d), the heat treatment is performed at 900-1100 degrees C for 3-24 hours. Preferred Components: The nanocomposite cathode active material produced in step (d) has an average particle diameter of 10-100 (preferably 10-80) nm accounts for at least 70 wt.% of the total weight of the nanocomposite cathode active material. The lithium compounds are lithium carbonate or lithium hydroxide. The manganese compound is manganese(III) oxide, manganese(II) oxide, and/or manganese oxide. EXAMPLE - Manganese oxide and lithium manganese oxide were uniformly pulverized by a mechanochemical process, and the mixture was heat treated in air at 500 degrees C for 12 hours to prepare lithium manganese oxide as a first cathode active material having an average particle diameter of 50 nm. Separately, a mixed solution of nickel sulfate/manganese sulfate/copper sulfate in a molar ratio of 0.5:0.3:0.2 was mixed with a sodium hydroxide solution and aqueous ammonia while maintaining the temperature at 60 degrees C, and the resulting mixture was allowed to react at a pH of less than or equal to 11 to prepare nickel-manganese-copper hydroxide ((Ni(0.5)Mn(0.3)Co(0.2))(OH)2) as a coprecipitated hydroxide having an average particle diameter of 70 nm. The molarity of the sodium hydroxide solution was adjusted to two times that of the mixed solution of nickel sulfate/manganese sulfate/copper sulfate. The coprecipitated hydroxide was washed with water ten times, filtered and dried at 150 degrees C for 24 hours. The coprecipitated hydroxide and lithium carbonate were homogenized, and heat treated in air at 800 degrees C for 12 hours to prepare lithium-manganese-copper oxide complex (LiNi(0.5)Mn(0.3)Co(0.2)O2) as a homogeneous second cathode active material having an average particle diameter of 60 nm. Thereafter, the cathode active materials lithium manganese oxide and lithium-manganese-copper oxide complex were homogenized in a molar ratio of 0.5:0.5 by a mechanochemical process, and the mixture was heat treated in air at 1000 degrees C for 12 hours and worked up to afford nanocomposite cathode active material.