To provide a multiple oxide which exhibits excellent battery performance when it is used as a positive active material of a lithium ion secondary battery; and to provide the lithium ion secondary battery using the same.

The multiple oxide suitable as the positive electrode active material of the secondary battery has a lamellar structure having a chemical composition of LiaNixMnyCozO2+b (wherein, x + y + z = 1; a is >1.00 and <1.3; and b is ≥0 and <0.3) and is characterized in that the diffraction peak angles on the (003) plane and the (104) plane in terms of the Miller indices hkl in the powder X-ray diffraction using Cu-Kα line are ≥18.65° and ≥44.50°, respectively, the half value width of the diffraction peak on each plane is ≤0.18°, further, the diffraction peak angles on the (108) plane and the (110) plane are ≥64.40° and ≥65.15°, respectively, and the half value width of the diffraction peak on each plane is ≤0.18°.