NOVELTY - A non-aqueous electrolyte secondary battery comprises: a positive electrode (1) containing a positive electrode active material; a negative electrode containing a negative electrode active material; and a non-aqueous electrolyte (4), where the positive electrode active material comprises a lithium-nickel-manganese composite oxide having a hexagonal layered rock-salt structure that belongs to the space group and containing lithium in 3b sites that contain transition metals.    USE - As non-aqueous electrolyte secondary battery (claimed) used as power sources for hybrid electric vehicles; and in portable electronic devices such as mobile telephones, camcorders, and notebook computers.    ADVANTAGE - The non-aqueous electrolyte secondary 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. The use of the lithium-nickel-manganese composite oxide as the positive electrode active material achieves excellent initial charge-discharge efficiency and discharge capacity in a battery that exhibits excellent regenerative power characteristics.    DETAILED DESCRIPTION - A non-aqueous electrolyte secondary battery comprises: a positive electrode containing a positive electrode active material; a negative electrode containing a negative electrode active material; and a non-aqueous electrolyte, where the positive electrode active material comprises a lithium-nickel-manganese composite oxide having a hexagonal layered rock-salt structure that belongs to the space group R-3m and containing lithium in 3b sites that contain transition metals. The lithium-nickel-manganese composite oxide is of formula Li(LixNiyMnz)O2-a, where x is 0-0.4, y is 0.3-0.4, z is 0.3-0.62, and a is 0-0.5.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic cross-sectional view of three-electrode beaker cell.    Positive electrode (1)    Counter electrode (2)    Reference electrode (3)    Electrolyte (4)