NOVELTY - Positive electrode active material (A) for a non-aqueous electrolyte secondary battery, comprises a lithium-containing transition metal oxide (I) having a closest-packed cubic structure of oxygen.    USE - (I) is useful for a non-aqueous electrolyte secondary battery, which is useful as power sources: for driving electronic equipment, such as notebook computers, mobile phones, and digital still cameras; and for equipment that are required to have high output, such as power storage equipment and electric automobiles and in households.    ADVANTAGE - (I) provides the battery having high charge and discharge capacities, high level of safety, and high reliable particularly when charged at high temperatures and high voltages, where the battery is excellent in load characteristics and cycle life.    DETAILED DESCRIPTION - Positive electrode active material for a non-aqueous electrolyte secondary battery comprises a lithium-containing transition metal oxide having a closest-packed cubic structure of oxygen, where the lithium-containing transition metal oxide has a structure of formula (Li(Lip(NixMnyCoz)1-p)O2) (I).    x, y, z = element contents of Ni, Mn and Co, respectively, and satisfies 0.2+y less than or equal to x less than or equal to 0.7, 0.15 less than or equal to y, 0.05 less than or equal to z, x+y+z is 1 or p is 0-0.1.    INDEPENDENT CLAIMS are included for:    (1) a non-aqueous electrolyte secondary battery comprising (A), a negative electrode, and a non-aqueous electrolyte; and    (2) a method for producing (A) comprising: preparing a precursor by a coprecipitation method performed by adding drop wise an aqueous alkaline solution into an aqueous acidic solution containing nickel ion, manganese ion, and cobalt ion; and mixing the precursor and lithium carbonate and baking the resultant mixture to prepare a particle of lithium-containing transition metal oxide with nickel, manganese, and cobalt evenly dispersed in it.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic illustration of an apparatus for synthesizing a precursor of positive electrode active material by a coprecipitation method.