Hemithioindigo hemistilbene (HTI) can be selectively photoisomerized from the Z-isomer into the E-isomer and vice versa. Using quantum chemical calculations, we have investigated the mechanism of the photoisomerization in detail. Our calculations demonstrate that two Z-and E-isomers exist in the electronic ground state as well as on the S-1 surface. The S-1 isomers are separated by small energy barriers along the dihedral twisting coordinate, but also a conical intersection with the electronic ground state is present at about 90 degrees twisting angle. Comparison with previously published experimental data reveals that most excited molecules, however, do not isomerize but instead relax to the equilibrium structure of the Z-isomer on the S-1 surface and return back to the ground state via regular fluorescence. Only a small fraction of the excited state population decays via the identified conical intersection and forms ground state E-isomers. This explains the comparably long lifetime of 38 ps of the excited FM molecules and the observed low quantum yield of photoswitching.