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Addresses solutions to the problem of reaching agreement in the presence of faults. Whereas the need for agreement has surfaced mainly in fault-tolerant real-time applications, agreement can be a useful mechanism in network security to mask intrusions. However, due to the communication overhead involved and the fact that the system is expected to operate without problems most of the time, early stopping algorithms are of special interest. We introduce a non-authenticated early stopping algorithm that is optimal in terms of rounds and the number of processors in the system. The basic idea of the algorithm as closely related to the work of P. Berman et al. (1992). However, our algorithm is easier to implement because of its algorithmic definition. It is directly derived from the algorithm by L. Lamport et al. (1982) and is based on two simple functions only. We are convinced that the construction of the early stopping algorithm presented in this paper increases understanding and clarifies the underlying problems of early stopping.