PROBLEM TO BE SOLVED: To provide: a complex metal oxide which enables the improvement in battery performance of sodium secondary batteries; a positive electrode active material including the complex metal oxide; a positive electrode fabricated by use of the positive electrode active material; and a sodium secondary battery having the positive electrode.SOLUTION: A complex metal oxide is expressed by a particular general formula and comprises an oxide having a P2 structure. A positive electrode active material is manufactured by use of the complex metal oxide. A positive electrode is manufactured by use of the positive electrode active material. A sodium secondary battery is manufactured by use of the positive electrode.