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The paper improves the conventional bottom-up algorithm for enumerating minimal cut sets of fault tree. It is proved that, when the logical product of two reduced sum-of-product forms is expanded by the distribution rule, one need only check if each resulting term is absorbed by some terms of two original sum-of-product forms. The algorithm for executing this process is presented and illustrated by an example. The entire computer program is given in a supplement and the computational results for several examples are presented to demonstrate the efficiency of the algorithm.