In this correspondence a complete decoding algorithm for double-error-correcting binary BCH codes of lengthn = 2^m - 1is introduced. It corrects all patterns of one and two errors and all patterns of three errors that belong to cosets that have a coset leader of weight three. This algorithm is based on the step-by-step decoding algorithm introduced by Prange and the decoding algorithm introduced by Meggitt, which makes use of the cyclic properties of the code. A comparison between this method and previously existing ones is also given.