A positive electrode active material for a secondary battery contains a spinel lithium manganese composite oxide expressed by a general formula of Li_a(M_xMn_2-x-yA_y)O₄ where x and y are positive values which satisfy 0.4x, 0y, x+y2, and 0a1.2. "M" denotes Ni and at least one metal element selected from the group consisting of Co, Fe, Cr and Cu. "A" denotes at least one metal element selected from the group consisting of Si and Ti. The ratio y of A has a value of 0.1y in case where A includes only Ti. Accordingly, it is possible to acquire a material for the positive electrode of a lithium ion secondary battery, which has a high capacity and a high energy density with a high voltage of 4.5 V or higher with respect to Li.