NOVELTY - Non-aqueous electrolyte secondary battery (I), comprises: a positive electrode containing a positive electrode active material comprising a lithium-containing oxide active material; a negative electrode; and a non-aqueous electrolyte, where the: lithium-containing oxide active material is lithium magnesium complex compound (a); and the lithium-containing oxide active material has a main peak at 2 theta = 17.95-18.15 degrees , as determined by an X-ray powder crystal diffraction measurement (copper (Cu) k alpha ).    USE - (I) is useful: in mobile information terminal devices, which are mobile telephones, notebook computers and personal digital assistants; and in power tools, power assisted bicycles, and electric vehicles (EVs) and hybrid EVs.    ADVANTAGE - (I) achieves high capacity. The method inhibits side reactions during charge and discharge by suppressing formation of an impurity similar to dilithium manganese trioxide (Li2MnO3) and prevents the discharge potential from decreasing even when lithium is added.    DETAILED DESCRIPTION - Non-aqueous electrolyte secondary battery (I), comprises: a positive electrode containing a positive electrode active material comprising a lithium-containing oxide active material; a negative electrode; and a non-aqueous electrolyte, where the: lithium-containing oxide active material is lithium magnesium complex compound of formula (LiaMgbMO(2 plus minus alpha ) (a); and the lithium-containing oxide active material has a main peak at 2 theta = 17.95-18.15 degrees , as determined by an X-ray powder crystal diffraction measurement (copper (Cu) k alpha ).    a = 0.65-1.05;    b, alpha = 0-0.3, preferably 0-0.2; and    M = at least one of manganese or cobalt.    An INDEPENDENT CLAIM is also included for a method of manufacturing (I), comprising: subjecting a sodium-magnesium-containing oxide of formula (NacMgbMO(2 plus minus alpha ) (b), to ion-exchange of sodium for lithium by using a molten salt, aqueous solution or an organic solvent, to prepare a positive electrode active material; preparing a positive electrode active material slurry containing the positive electrode active material and a binder, and then applying the positive electrode active material slurry to a positive electrode current collector, to prepare a positive electrode; interposing a separator (3) between the positive electrode and a negative electrode to prepare a power-generating element; and encasing the power-generating element in a battery case, and filling an electrolyte solution in the battery case.    c = 0.65-0.75.    DESCRIPTION OF DRAWING(S) - The figure is a cross-sectional view of a test cell.    Working electrode (1)    Counter electrode (2)    Separator (3)    Reference electrode (4)    Test cell container (5)