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Modular inversion operation is commonly used in realizing the public key cryptosystem. A rapid and general algorithm(RGA) is presented. It can be implementated in recursion and non-recursion form. It can be used to evaluate modular inversion of any integer. The result of the algorithm is its modular inversion or showing that its modular inversion doesn't exist. The recursive times that the algorithm needs are few. Theoretical proof and analysis of the algorithm are given. Experiment results show the effect of the new algorithm.