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The main goal of a fault-tree algorithm is to obtain the minimal cut sets as quickly as possible. This paper presents a new algorithm for cut-set reduction; it is based on the partition of the cut sets into two families: Those containing repeated events, and others. It is proved that only those containing repeated events need reduction. This algorithm was implemented by a computer program which had been associated with MOCUS algorithm, both developed on a microcomputer. This algorithm can be combined with other reduction algorithms. We believe that this algorithm is efficient.