Let $A=\{1,\dots,k\}$, let $P=(P_{ij})$ be a stochastic matrix on $A$, let $\pi$ be a stationary probability vector satisfying $\pi P=\pi$, and let $\mu_{\pi,P}$ be the associated stationary Markov measure on $A^{\mathbb Z}$. Then $h_{\mu_{\pi,P}}(\sigma)= -\sum_{i \in A} \pi_i\sum_{j \in A : P_{ij}>0} P_{ij}\log P_{ij}$, where terms with $P_{ij}=0$ are omitted.