Formula _(1): wherein K n ABO _m [wherein, A represents a bivalent element of group 7 to 11 periodic table. B shows +4 of silicon, germanium, titanium or manganese. However, when A is titanium B manganese, A excluding the case B with cobalt is silicon. n represents an 1.5 to 2.5. m represents a 3.5 to 4.5. Potassium compound represented by], and by adopting a positive active material for potassium ion secondary battery containing the same, a positive electrode active material (particularly the positive electrode active for potassium ion secondary battery potassium secondary battery other than Prussian blue providing a material which can be used as material).