The exact Green function for a particle moving between two static reversible traps in one dimension is obtained for the continuous diffusion model. From this function, we derive the exact expressions of various survival probabilities, which are the key elements in devising the efficient Brownian dynamics algorithm. An exact expression of the mean survival probability is also obtained for the periodic distribution of reversible traps both for the crossing-allowed and crossing-forbidden cases. For the random distribution of reversible traps, the exact mean survival probability is obtained only for the crossing-forbidden case and its long time behavior is compared with that of the crossing-allowed case. We find, in this case, that not only the long time asymptotic relaxation behavior but also the equilibrium concentration itself can be changed from the classical results due to the fluctuation effect of the trap density.