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A new upper hound and lower hound are developed for the rate-distortion function of a binary symmetric Markov source with respect to the frequency of error criterion. Both hounds are explicit in the sense that they do not depend on a blocklength parameter. In the interval , where is Gray's critical value of distortion, is convex downward and possesses the correct value and the correct slope at both endpoints. The new lower bound diverges from the Shannon lower bound at the same value of distortion as does the second-order Wyner-Ziv lower bound. However, it remains strictly positive for all and therefore eventually rises above all the Wyner-Ziv lower bounds as approaches . Some generalizations suggested by the analytical and geometrical techniques employed to derive and are discussed.