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In this paper, a novel fault-tolerant algorithm for achieving approximate Byzantine consensus in asynchronous networks is proposed. It is shown that the topological condition required for the success of the algorithm is more relaxed than the previous results. We prove that the synchronicity of the network does not affect this condition and the algorithm succeeds in synchronous networks as well. The same fact is concluded in networks with delay on communication paths. Finally, we extend the results to networks with time-varying underlying graph.