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PROBLEM TO BE SOLVED : To provide a sodium secondary battery that can reduce the amount of rare metal elements, such as lithium and cobalt, used and has a larger discharge capacity after the repetition of charge and discharge than the conventional one and a composite metal oxide usable as a positive electrode active material for the sodium secondary battery. SOLUTION : The composite metal oxide comprises Na, Mn and M1(wherein M1is Fe or Ni) and has an Na : Mn : M1molar ratio of a : (1-b) : b (wherein a is a value in the range of more than 0.5 and less than 1 and b is a value in the range of not less than 0.001 and not more than 0.5). The composite metal oxide is represented by formula (1) : NaaMn1-bM1bO2(wherein M1, a and b are same as above, respectively). The positive electrode active material for the sodium secondary battery comprises the composite metal oxide. COPYRIGHT : (C)2009, JPO&INPIT