The intersystem crossing from S-1 to T-1 in glyoxal induced by the collision of Ar has been studied theoretically. In particular, we have focused on the effects of the intermolecular spin-orbit interaction, which was not considered important in this process. The interaction potential of S-1 in the glyoxal and Ar system was carried out by the CASSCF method. Further, the interaction potential of T-1 and the spin-orbit interaction, which is represented by the Breit-Pauli Hamiltonian, between S-1 and T-1 were calculated by the full-CI method with the same active spaces and molecular orbitals as those of the CASSCF calculations for S-1. Using these calculation results, the semiclassical dynamics calculations were employed to estimate the transition cross sections and rate constants. It is found that the intermolecular spin-orbit interaction largely amplifies the transition probabilities and the relaxation on the T-1 state is indispensable to describing the dynamics in this intersystem crossing.