Because of the composition represented by General Formula: Li.sub.1+x+.alpha.Ni.sub.(1-x-y+.delta.)/2Mn.sub.(1-x-y-.delta.)/2M.sub.y- O.sub.2 (where 0.ltoreq.x.ltoreq.0.05, -0.05.ltoreq.x+.alpha..ltoreq.0.05, 0.ltoreq.y.ltoreq.0.4; -0.1.ltoreq..delta..ltoreq.0.1 (when 0.ltoreq.y.ltoreq.0.2) or -0.24.ltoreq..delta..ltoreq.0.24 (when 0.2.ltoreq.y.ltoreq.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.