A large unexamined second-order nonlinear optical (NLO) process is found in a 4-N,N-dimethylamino-4'-N'-methyl stilbazolium tosylate (DAST) crystal, which has a large figure of merit among NLO crystals. In second-order NLO processes using a DAST crystal, the χ111(2) process of light excitation is commonly used, involving a-axis polarized light excitation with light generation of a-axis polarized light. However, there have been few studies of other second-order NLO susceptibility processes to date. In this Letter, terahertz (THz) wave generation via second-order NLO processes based on the χ133(2) second-order NLO susceptibility of the DAST crystal was investigated. By adjusting the polarization direction of the excitation light using a prism-coupled Cerenkov phase-matching method, efficient generation of THz waves was achieved using a process involving χ133(2). The magnitude of the NLO constant χ133(2) estimated from the THz intensity ratio was 77.8 pm/V. These results indicate that prism-coupled Cherenkov phase matching can be used to identify undiscovered NLO processes for NLO crystals.