NOVELTY - The 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. 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.    USE - The non-aqueous electrolyte secondary battery is useful as power sources for hybrid electric vehicles, and portable electronic devices such as mobile telephones, camcorders and notebook computers.    ADVANTAGE - The non-aqueous electrolyte secondary battery can be economically manufactured, exhibits high initial charge-discharge efficiency, high discharge capacity and excellent regenerative power characteristics, and provides good balance between input power and output power.    DETAILED DESCRIPTION - The 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. 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 expressed as Li(LixNiyMnzM-b)O2-a, where: x is 0-0.4; y is 0.12-0.5; z is 0.3-0.62; a is 0-0.5; and M is metal element having a valency of 2-6. The variables x, y, z and b satisfy the expressions of x greater than (1-2y)/3, one quarter less than y/z 1, 0 less than b/(y+z) less than 0.1 and 1 less than x+y+z+b less than 1.1. The capacity ratio of the negative electrode to the positive electrode (negative electrode charge capacity/positive electrode charge capacity) is greater than or equal to 1.0 when the battery is charged until the potential of the positive electrode reaches greater than or equal to 4.45 V.