NOVELTY - Manufacturing a composite positive active material comprises acid-treating an overlithiated lithium transition metal oxide (I) or (II) and applying fluorine onto the acid-treated overlithiated lithium transition metal oxide.    USE - The method is useful for manufacturing a composite positive active material which is useful in a positive electrode of a lithium battery (all claimed) which is useful for electric vehicles requiring a high capacity battery, a high-power output, and high temperature operation, in addition to existing mobile phones, portable computers, electric bicycles and power tools.    ADVANTAGE - The method: provides the positive active material having a high capacity; and makes the composite positive active material that improves a rate property.    DETAILED DESCRIPTION - Manufacturing a composite positive active material comprises acid-treating an overlithiated lithium transition metal oxide of formula (I) or (II) and applying fluorine onto the acid-treated overlithiated lithium transition metal oxide.    M1 = at least one transition metal having an average oxidation number of +4 comprising Groups 4 or 5 transition metals;    M2 = Groups 4 or 5 transition metals having an average oxidation number +3;    M3 = at least one transition metal having mixed average oxidation numbers +3 and +4 comprising Groups 4 or 5 transition metals;    x, x1, x2 = greater than 0 to less than 1;    x+x1+x2 = 1; and    d = 0-0.33.    INDEPENDENT CLAIMS are also included for:    (1) the composite positive active material manufactured by the method; and    (2) a lithium battery (30) comprising a positive electrode (23) comprising the composite positive active material, a negative electrode (22) disposed opposite to the positive electrode, and an electrolyte disposed between the positive electrode and the negative electrode.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of a lithium battery.    Negative electrode (22)    Positive electrode (23)    Battery case (25)    Encapsulation member (26)    Lithium battery (30)