Lithium-containing composite oxide and nonaqueous secondary cell using the same, and method for manufacturing the same

1+x+α(1−x−y+δ)/2(1−x−y−δ)/2y2 Because of the composition represented by General Formula: LiNiMnMO(where 0≦x≦0.05, −0.05≦x+α≦0.05, 0≦y≦0.4; −0.1≦δ≦0.1 (when 0≦y≦0.2) or −0.24≦δ≦0.24 (when 0.2≦y≦0.4); and M is at least one element selected from the group consisting of Ti, Cr, Fe, Co, Cu, Zn, Al, Ge and Sn), a high-density lithium-containing complex oxide with high stability of a layered crystal structure and excellent reversibility of charging/discharging can be provided, and a high-capacity non-aqueous secondary battery excellent in durability is realized by using such an oxide for a positive electrode.