NOVELTY - A composite positive active material comprises an over-lithiated lithium transition metal oxide (I) or (II).    USE - Composite positive active material is used for positive electrode of lithium battery (claimed). Uses include but are not limited to mobile phones, portable computers, electric vehicles and hybrid vehicles.    ADVANTAGE - The positive electrode containing composite positive active material provides lithium battery with high capacity and excellent durability.    DETAILED DESCRIPTION - A composite positive active material comprises an over-lithiated lithium transition metal oxide of formula: xLi2-yM"yMO3-(1-x)LiM'O2 (I) or xLi2-yM"yMO3-x'LiM'O2-x"Li1+dM"'2-dO4 (II).    M=metal chosen from period 4 transition metals and period 5 transition metals, and having average oxidation number of +4;    M'=metal chosen from period 4 transition metals and period 5 transition metals, and having average oxidation number of +3;    M"=metal cation chosen from period 2 to period 7 elements;    x,x',x"=more than 0 and less than 1;    y=0-1 (excluding 0);    M"'=metal chosen from period 4 transition metals and period 5 transition metals, and having average oxidation number from +3 to +4;    x+x'+x"=1;and    d=0-0.33.    INDEPENDENT CLAIMS are included for the following:    (1) lithium battery (30), which comprises a positive electrode (23) comprising the composite positive active material, a negative electrode (22) opposing the positive electrode, and an electrolyte between the positive electrode and the negative electrode; and    (2) preparation of composite positive active material, which involves treating the over-lithiated lithium transition metal oxide with an acid, and doping the acid-treated over-lithiated lithium transition metal oxide with a metal cation.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic perspective view of lithium battery.    Negative electrode (22)    Positive electrode (23)    Separator (24)    Battery case (25)    Lithium battery (30)