In this paper, we discuss two processes for detecting the pure triangle singularity effect through the decays of $\psi(2S)$. The triangle singularity is proposed around 1959, but until now there is no confirmed experimental evidence. Thus, we explore the $\psi(2S)\to p\bar{p}\eta$ and $\psi(2S)\to \pi^+\pi^-K^+K^-$ processes to predict the pure triangle singularity effect by a model independent calculation. From these studies, we find that it needs to choose a proper width of the intermediate particle around several MeV, which will be the best place to find the signal of the triangle singularity effect.