A non-aqueous electrolyte rechargeable battery including: (a) a positive electrode capable of charging and discharging lithium; (b) a negative electrode capable of charging and discharging lithium; (c) a separator or a lithium ion conductive layer interposed between the positive electrode and the negative electrode; and (d) a lithium ion conductive non-aqueous electrolyte, wherein the positive electrode contains a mixture of a first positive electrode active material and a second positive electrode active material, the first positive electrode active material includes lithium oxide containing manganese, the lithium oxide further contains aluminum and/or magnesium, and the second positive electrode active material includes Li.sub.xCo.sub.1-y-zMg.sub.yAl.sub.zO.sub.2 where 1.ltoreq.x.ltoreq.1.03, 0.005.ltoreq.y.ltoreq.0.1 and 0.001.ltoreq.z<0.02.