NOVELTY - Forming a carbon coating, comprises heat-treating (S120) a lithium transition metal composite oxide (I) in an atmosphere of a gas mixture including carbon dioxide and at least one of an alcohol compound (II), an alkene compound (III), and a metal oxide compound (IV).    USE - The method is useful for forming a carbon coating on a composite metal oxide such as a positive electrode active material for a lithium rechargeable battery (all claimed), which is useful in electrical power storages/electric vehicles.    ADVANTAGE - The method is capable of simply forming the carbon coating on the positive electrode active material without structural deformation of the material, thus improving performance, life span, energy density and high-temperature storage characteristics of the battery.    DETAILED DESCRIPTION - Forming a carbon coating, comprises heat-treating (S120) a lithium transition metal composite oxide of formula (I) in an atmosphere of a gas mixture including carbon dioxide and at least one of an alcohol compound of formula (CnH(2n+-t)(OH)t) (II), an alkene compound of formula (Cn1H(2n1)) (III), and a metal oxide compound of formula (Li(0.9+a)MbM1cN1dOe) (IV).    M, M1 = Ni, Co, Mn, Mo, Cu, Fe, Cr, Ge, Al, Mg, Zr, W, Ru, Rh, Pd, Os, Ir, Pt, Sc, Ti, V, Ga, Nb, Ag, Hf, Au, Cs, B, or Ba;    N1 = Ni, Co, Mn, Mo, Cu, Fe, Cr, Ge, Al, Mg, Zr, W, Ru, Rh, Pd, Os, Ir, Pt, Sc, Ti, V, Ga, Nb, Ag, Hf, Au, Cs, B (where N1 is different from M and M1) or Ti, V, Si, B, F, S, or P, where at least one of M, M1 and N1 is Ni, Co, Mn, Mo, Cu, or Fe;    n = 1-20;    t = 0 or 1;    n1 = 2-6;    a = 0-1.6;    e = 1-4; and    b-d = 0-2, where b, c and d are not simultaneously equal to 0.    INDEPENDENT CLAIMS are included for:    (1) a composite metal oxide of formula (II) having a uniform carbon coating; and    (2) a rechargeable lithium battery comprising a positive electrode active material comprising (II) and a carbon coating uniformly formed on the composite metal oxide.    DESCRIPTION OF DRAWING(S) - The figure shows a flow chart of a method for forming a carbon coating.    Obtaining lithium transition metal composite oxide (S100)    Optionally heat-treating the lithium transition metal composite oxide under an inert gas atmosphere (S110)    Heat-treating the lithium transition metal composite oxide in an atmosphere of a gas mixture including carbon dioxide and hydrocarbon to form a carbon coating (S120)    Cooling the carbon-coated metal composite oxide, optionally under an inert gas atmosphere. (S130)