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Safe reinforcement learning (RL) is still very challenging since it requires the agent to consider both return maximization and safe exploration. In this paper, we propose CUP, a Conservative Update Policy algorithm with a theoretical safety guarantee. We derive the CUP based on the new proposed performance bounds and surrogate functions. Although using bounds as surrogate functions to design safe RL algorithms have appeared in some existing works, we develop them at least three aspects: (i) We provide a rigorous theoretical analysis to extend the surrogate functions to generalized advantage estimator (GAE). GAE significantly reduces variance empirically while maintaining a tolerable level of bias, which is an efficient step for us to design CUP; (ii) The proposed bounds are tighter than existing works, i.e., using the proposed bounds as surrogate functions are better local approximations to the objective and safety constraints. (iii) The proposed CUP provides a non-convex implementation via first-order optimizers, which does not depend on any convex approximation. Finally, extensive experiments show the effectiveness of CUP where the agent satisfies safe constraints. We have opened the source code of CUP at https://github.com/RL-boxes/Safe-RL.