The use of hydrofluorocarbons (HFCs) as refrigerants in air-conditioning and refrigeration systems is being re-examined globally due to their high Global Warming Potential (GWP) and large environmental load. Next-generation refrigerants with low GWP are currently attracting a lot of attention as a replacement for conventional refrigerants. Recently, we have developed a novel refrigerant, trans-1,2-difluoroethylene (R-1132(E)), which has similar saturated vapor pressure to R-32 and an extremely low GWP value of 0.0056. R-474A and R-479A, refrigerants containing R-1132(E), are already registered with ASHRAE standard 34 and ISO 817 and are expected to become next-generation refrigerants. However, due to chemical stability issues, a self-decomposition reaction of R-1132(E) can occur. For this study, both R-1132(E) and the blend of R-1132(E) and R-1234yf have been investigated. We have developed methods for evaluating the self-decomposition reaction for three ignition sources that may occur in air conditioners and clarified the conditions under which the self-decomposition reaction of R-1132(E) and R-1234yf blends does not occur.