NOVELTY - A positive electrode active material comprises lithium-transition metal composite oxide containing nickel, cobalt and manganese, and having a hexagonal crystalline structure. The transition metal (Me) of the lithium-transition metal composite oxide contains nickel (Ni), cobalt (Co) and manganese (Mn) in preset molar ratios. The value obtained by dividing the half-width ratio (F(003)/F(104)) at potential of 4.3 V (vs. Li/Li+) by the half-width ratio (F(003)/F(104)) at potential of 2.0 V (vs. Li/Li+) is 0.9-1.1.    USE - Positive electrode active material is used for forming electrodes for lithium secondary batteries for electrical storage apparatus (all claimed) for electric vehicles, hybrid vehicles and plug-in hybrid motor vehicles.    ADVANTAGE - The positive electrode active material provides lithium secondary batteries with high energy density, excellent initial stage efficiency.    DETAILED DESCRIPTION - A positive electrode active material comprises lithium-transition metal composite oxide containing nickel, cobalt and manganese, and having a hexagonal crystalline structure. The molar ratios of nickel (Ni), cobalt (Co) and manganese (Mn) in the transition metal (Me) of lithium-transition metal composite oxide satisfies the relations: 0.5 less than or equal to (Ni/Me) less than or equal to 0.9, 0.1 less than or equal to (Co/Me) less than or equal to 0.3, and 0.03 less than or equal to (Mn/Me) less than or equal to 0.3. The value obtained by dividing the half-width ratio (F(003)/F(104)) at potential of 4.3 V (vs. Li/Li+) by the half-width ratio (F(003)/F(104)) at potential of 2.0 V (vs. Li/Li+) is 0.9-1.1. An INDEPENDENT CLAIM is included for manufacture of positive electrode active material.    DESCRIPTION OF DRAWING(S) - The drawing shows an external perspective view of the lithium secondary battery.    Lithium secondary battery (1)    Battery container (3)    Positive electrode terminal (4)    Positive electrode lead (4')    Negative electrode terminal (5)