In this Letter, we report on ab initio non-adiabatic coupling terms, the relevant conical intersection (ci)-points and the corresponding adiabatic potentials as obtained for the C2H2 (acetylene) molecule. The emphasis in this study is on the region, where the four lower A'-states of this molecule form three (in fact four) cis all located close to each other so that if the molecule is excited to the fourth state it may decay to its ground state without the intervention of spin-orbit couplings. (c) 2005 Elsevier B.V. All rights reserved.