Being monolithic with its connected links, the flexure hinge has been widely used for precision engineering where high accuracy is demanded because it has zero friction and backlash. In real application, the flexure hinge is often subjected to periodic loadings, which make it a necessity for its fatigue analysis. In this study, we discussed the fatigue properties of the right circular flexure hinge (RCH). The accurate estimation of the maximum stress in RCH under a certain load is firstly derived. After that, the Stress-Life (S-N) curve was derived from the results of fatigue tests. The design S-N curve (lower-bound S-N curve) was calculated by using the one-sided tolerance limit that derived based on the approximate Owen tolerance limit method. Finally, the effects of the hinge parameters, e.g., the radius r and the thickness t, on the fatigue performance of the RCH were discussed.