The energies and derivative couplings are computed in the vicinity of the 1(2)A'-2(2)A' seam of conical intersections for AlH2. It is shown that the reaction path for the decomposition of excited vibrational levels of AlH2(X(2)A(1)) to Al + H-2 passes quite close to the minimum energy crossing point (MECP), the minimum energy point on the seam of conical intersections. Near the MECP the seam of conical intersections exhibits an unusual trifurcation with a C-2v portion dividing into a branch that preserves C-2v symmetry and two symmetry equivalent branches that have only C-s symmetry.