While a wealth of studies exist on the potential energy surface (PES) for the F + H2 reaction, exploration of the effect of conical intersections (CIs on the corresponding adiabatic PES has only been initiated. In this respect, a recent emphasis on the specific role of the Jahn-Teller (JT) CI between the two lowest states has shown that the adiabatic-to-diabatic transformation (ADT) angle (mixing angle), γ12, between these two states deviates largely from its quantized value of π for configuration spaces with F close to the H-H system. Hence, investigating the effect of the other CIs present, involving the higher states, on the reactive channel is necessary. In this article, we report for the first time the collinear (2, 3), (3, 4) and (4, 5) JT CIs in this system and also reveal their major effects on γ12, which is instrumental in the diabatization of the PES for the title reaction system. © 2012 Elsevier B.V. All rights reserved.