The radiationless decay of T-1 norbornene to the singlet ground state is studied using density-functional and ab initio CASSCF calculations of the potential energy surface crossing and of the spin-orbit coupling. The rate of decay is predicted using two approximate multi-dimensional non-adiabatic methods, one of which is based on Fermi's Golden Rule, and the other is a version of RRKM theory adapted for non-adiabatic processes. Unlike a previous Landau-Zener treatment of this process by some of us [Chem. Phys. Lett. 287 (1998) 602-607], both methods correctly predict a short lifetime for the triplet excited state, in reasonable agreement with experimental data. This underlines the importance of tunnelling in non-radiative relaxation processes.