; Li Xue-Qian] Nankai Univ, Dept Phys, Tianjin 300071, Peoples R China
; [Ke Hong-Wei] Tianjin Univ, Dept Phys, Tianjin 300072, Peoples R China
; [Ding Yi-Bing] Chinese Acad Sci, Grad Univ, Dept Phys, Beijing 100049, Peoples R China
; [Shen Peng-Nian] CAS, Inst High Energy Phys, Beijing 100049, Peoples R China
Besides using the laser beam, it, is Very tempting to directly testify the Bell inequality at high energy experiments where the spin correlation is exactly what, the original Bell inequality investigates. In this work, we follow the proposal raised in literature and use the successive decays J/psi -> gamma eta(c) -> Lambda(Lambda) over bar -> p pi(-)(p) over bar pi(+) to testily the Bell inequality. Our goal is twofold, namely, we first make a Monte-Carlo simulation of the processes based on the quantum field theory (QFT). Since the underlying theory is QFT, it implies that we pre-admit the validity of quantum picture. Even though the QFT is true, we need to find how big the database should be. so that we can clearly show deviations of the correlation from the Bell inequality determined by the, local hidden variable theory. There have been some critiques on the proposed method, so in the second part, we suggest some improvements which may help to remedy the ambiguities indicated by the critiques. It may be realized at an updated facility of high energy physics, such as BES III.