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The problem of finding all the critical paths is a mathematics based algorithm for scheduling a set of project activities. A new algorithm to find all the critical paths for an AOE network is presented in this paper. With this algorithm, topological inverted sequence scanning is not required again. A predecessors list is designed for each event node to record the earliest starting time and itpsilas predecessors in the longest path. The data structure used in this algorithm is more simple and it can be realized more easily. The running time of this algorithm is O(n+e).