NOVELTY - The non-aqueous electrolyte secondary battery for power supply applications such as hybrid electric vehicles, comprises a positive electrode containing a positive electrode active material, a negative electrode containing a negative electrode active material, and a non-aqueous electrolyte. The positive electrode active material comprises a lithium-nickel-manganese composite oxide having a hexagonal layered rock-salt structure belonging to the space group R-3m and containing lithium in 3b sites having transition metals.    USE - Useful for power supply applications such as hybrid electric vehicles.    ADVANTAGE - The battery achieves a good balance between input power and output power, exhibits excellent power characteristics, and has high initial charge-discharge efficiency and a high discharge capacity.    DETAILED DESCRIPTION - The non-aqueous electrolyte secondary battery for power supply applications of hybrid electric vehicles, comprises a positive electrode containing a positive electrode active material, a negative electrode containing a negative electrode active material, and a non-aqueous electrolyte. The positive electrode active material comprises a lithium-nickel-manganese composite oxide having a hexagonal layered rock-salt structure belonging to the space group R-3m and containing lithium in 3b sites having transition metals. The lithium-nickel-manganese composite oxide is represented by the molecular formula Li(LixNiyMnz)O2-a, where M is a metal element, x is 0-0.4, y is 0.12-0.5, z is 0.3-0.62 and a is 0-0.5. The variables x, y, z satisfy the expressions of xless than or equal to(l-2y)/3, 1/4greater than or equal toy/zless than or equal to1.0 and x+y+z=1. The capacity ratio of the negative electrode to the positive electrode is 1 or greater when the battery is charged until the potential of the positive electrode reaches 4.45 V or higher.    DESCRIPTION OF DRAWING(S) - The diagram shows a three-electrode beaker cell:    Working electrode; (1)    Counter electrode; (2)    Reference electrode; (3)    Electrolyte solution. (4)