Because of the composition represented by General Formula: Li1+x+alphaNi(1-x-y+delta)/2Mn(1-x-y-delta)/2MyO2 (where 0<=x<=0.05, -0.05<=x+alpha<=0.05, 0<=y<=0.4; -0.1<=delta<=0.1 (when 0<=y<=0.2) or -0.24<=delta<=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.