We perform ab initio calculation using MOLPRO on the 22E ′ and 12A1′ states of Na3 cluster and explore for locating the point of conical intersections (CIs) in the configuration space (CS). The functional form of Non-Adiabatic Coupling Term (NACT) between the 22E′ states indicates the presence of singularity at four points in the CS. While performing Adiabatic-to-Diabatic Transformation (ADT) [Chem. Phys. Lett. 35 (1975) 112] by employing three state NACTs, two diagonal elements of ADT matrix display four sign changes as a signature of four CIs. Moreover, the locations of those CIs are confirmed by Longuet-Higgins' theorem. © 2011 Elsevier B.V. All rights reserved.