The mechanism of bifurcation along the reaction path on an adiabatic potential surface is discussed in terms of the second-order Jahn-Teller (SOJT) effect. From the viewpoint of this SOJT effect, bifurcation occurs due to the mixing of the nearest nontotally symmetric electronic excited state into the electronic ground state through a molecular vibration belonging to the same nontotal symmetry. Thus, the bifurcating region should be limited where the excited state comes close to the ground state. In order to demonstrate our SOJT theory of bifurcation, we calculated intrinsic reaction coordinates (IRC) of thioformaldehyde under C(s) symmetry constraint for the dissociation reaction to H-2+CS and for the isomerization reaction to thiohydroxycarbene (HCSH). Energies of the lowest excited electronic state (A") were also calculated along the IRC. These calculations were performed with 6-31G** basis sets at three different computational levels : (1) HF level, (II) SDCI level for HF geometries, and (III) full valence complete active space self-consistent field (CASSCF) level. As is expected from our theory, bifurcations observed for both dissociation and isomerization reactions at the HF level disappear at the CASSCF level due to the larger energy separation between ground and excited states. For the isomerization reaction, while the previous calculations at the HF level predicted that the transition state and IRC should have C1 symmetry, the transition state and IRC are proved to have C(s) symmetry at the CASSCF level as the result of the disappearance of bifurcation.