This new MTS-TSH algorithm has been tested successfully on the photorelaxation of protonated formaldimine. We have shown that the MTS-TSH method is able to recover the correct state population along the reaction path as well as the correct geometries at the transitions. For this MTS scheme (combining PBE/PBE0 forces and time step factors between 2 and 8) a speed-up between 1.5 and 3 could be achieved compared to standard FS-TSH simulations. The obtained speed-ups are actually very close to the ideal speed-up that could be obtained with the computational settings considered, indicating that a better performance could be reached by considering cheaper models as low level in the MTS scheme.