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In this paper, an ordering result is given for Markov channels with respect to mutual information, under the assumption of an independent and identically distributed (i.i.d.) input distribution. For those Markov channels in which the capacity-achieving input distribution is i.i.d., this allows ordering of the channels by capacity. The complexity of analyzing general Markov channels is mitigated by this ordering, since it is possible to immediately determine that a wide class of channels, with different numbers of states, has a smaller mutual information than a given channel.