Abstract: An improved process for preparing a spinel type lithium manganese composite oxide represented by the general formula (I): Lix Mn(2−y) My1 By2 O4 wherein M represents at least one member selected form among Al, Cr, Fe, Ni, Co, Ga, and Mg; 0.9≦x≦1.1; and y=y1+y2, wherein 0.002≦y≦0.5, 0≦y1≦0.5, and 0.002≦y2≦0.1 or represented by the general formula (Ia) Lix Mn(2−y) My O4, which is the same as the general formula (I) except that y2 is 0. In formula (Ia) M and x are each as defined above and 0.002≦y≦0.5; and a cathode active material for a lithium ion rechargeable battery comprising the spinel type lithium manganese composite oxide having improved charge-discharge characteristics produce by the above method. The composite oxide thus produce is a novel one improved in cycle characterized, particularly in charge-discharge cycle characterized in a high-temperature (50° C. or above) environment, and hence is very useful form the viewpoint of industry.