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Ifa is an age long divination system vastly consulted across west Africa, the Caribbeans and the Americas. The system goes with the use of signature codes named Odu Ifa which are 256 in number consisting of 16 Oju Odu (major) and 240 Omo Odu (minor). We consider the algebraic structure of this divination system by writing the codes representing the main Odu as 4 × 2 matrices which are found to satisfy group axioms under addition mod 2. We construct the Cayley table that gives an abelian group which we dubbed “self-inversed group”. Other properties of group structure are outlined.