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Byzantine Agreement involves a system of n processes, of which some t may be faulty. The problem is for the correct processes to agree on a binary value sent by a transmitter that may itself be one of the n processes. If the transmitter sends the same value to each process, then all correct processes must agree on that value, but in any case, they must agree on some value. An explicit solution not using authentication for n = 3t + 1 processes is given, using 2t + 3 rounds and O(t³ log t) message bits. This solution is easily extended to the general case of n ⩾ 3t + 1 to give a solution using 2t + 3 rounds and O(nt + t³ log t) message bits.