TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The acid-treating of the overlithiated lithium transition metal oxide is performed by using an acidic solution containing at least one acid comprising nitric acid (preferred), sulfuric acid, hydrochloric acid, citric acid, fumaric acid, maleic acid, boric acid or phosphoric acid. The method further comprises: drying the acid-treated overlithiated lithium transition metal oxide at a temperature of 100-200 degrees C after the acid-treating of the overlithiated lithium transition metal oxide and before the applying of the fluorine onto the acid-treated overlithiated lithium transition metal oxide; and heat-treating the fluorine-doped overlithiated lithium transition metal oxide at a temperature of 200-500 degrees C in air. The applying of the fluorine on the acid-treated overlithiated lithium transition metal oxide is performed by using a doping solution containing at least one fluorine compound comprising lithium fluoride, ammonium fluoride (both preferred), magnesium fluoride, strontium fluoride, beryllium fluoride, calcium fluoride, ammonium bifluoride or ammonium hexafluoroaluminate. Preferred Components: The overlithiated lithium transition metal oxide is of formula (xLi2MnO3-(1-x)LiNiaCobMncO2) (III).a, b, c = greater than 0 to less than 1; anda+b+c = 1.An average particle diameter of the overlithiated lithium transition metal oxide is 10 nm to 500 mu m. An amount of the fluorine compound is 0.01-10 wt.% based on a total amount of the doping solution. Preferred Definitions:    M1 = at least one metal comprising Mn, Ti, Zr, Sn or Mo; and    M2 = at least one metal comprising Ni, Co, Mn, Fe, Al, Mg, Zn, Cu, Cr, V or Nb.    EXAMPLE - Material having lithium manganate-lithium nickel-cobalt-manganese oxide composition (0.55Li2MnO3-0.45LiNi0.5Co0.2Mn0.3O2) was used as an overlithiated oxide. 10 g Overlithiated oxide was added to a 500 ml of 0.2 M nitric acid solution, and the reaction mixture was stirred for 4 minutes. The reaction mixture was filtered using a vacuum filter to remove the solvent, followed by being dried at a temperature of 120 degrees C, thus obtaining an acid-treated overlithiated oxide. 10 g Of the acid-treated overlithiated oxide was added to a 500 ml of 1 wt.% lithium fluoride solution, and the reaction mixture was stirred at a temperature of 50 degrees C for 24 hours. Subsequently, the reaction mixture was filtered using a vacuum filter to remove the solvent, followed by being dried at a temperature of 80 degrees C. Then, in a nitrogen atmosphere, the resultant product was subjected to heat treatment at a temperature of 300 degrees C for 5 hours. After completing the heat treatment, a fluorine-doped overlithiated oxide was obtained.