NOVELTY - A cathode active material comprises a composite transition metal oxide (I) which intercalates and deintercalates magnesium.    USE - Cathode active material is used for cathode for magnesium secondary battery (all claimed). Uses include but are not limited to video camera, mobile phone, electric vehicle, notebook personal computer, plug-in hybrid electric vehicle and smartphone.    ADVANTAGE - Since the structural stability of the composite transition metal oxide is improved, the durability of the magnesium battery including the cathode active material is improved. The structural stability of the composite transition metal oxide is improved during charge and discharge processes. Since the metal (Ma) and the metal (Mb) are simultaneously involved in the charge and discharge processes, the dissolution of the metal (Ma) is prevented due to excessive oxidation of the metal (Ma). The electroconductivity of the composite transition metal oxide is improved by substituting the transition metal oxide with the metal (Mb) which has high electroconductivity than the metal (Ma). Since the resistance of the cathode active material is decreased by improving the electroconductivity of the composite transition metal oxide, an overvoltage is decreased during the charge and discharge of the magnesium battery, and the reversibility of an electrode reaction is improved.    DETAILED DESCRIPTION - A cathode active material comprises a composite transition metal oxide of formula: MgxMa1-yMbyO2+d (I), where x is 0-1, y is 0.05-5, d is -0.3 or more to less than 1, and Ma and Mb are metal chosen from groups 5 to 12 of the periodic table, which intercalates and deintercalates magnesium. INDEPENDENT CLAIMS are included for the following:    (1) cathode (3); and    (2) magnesium secondary battery (1), which comprises the cathode, an anode (2) and an electrolyte comprising magnesium.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of the magnesium battery.    Magnesium battery (1)    Anode (2)    Cathode (3)    Separator (4)    Battery case (5)