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Assessing the quality of speech in communication systems is a very important issue. Traditionally, perceived speech quality has been measured by time-consuming and expensive human (subjective) listening tests. New computer-based objective methods that compare input and output speech records are not realizable in some cases, such as when the input speech is unavailable. So far, output-based objective methods that require only the received speech have received little attention in the literature. This paper proposes a new method of output-based objective speech quality measurement using continuous hidden Markov models (HMMs). A symmetric distance measure is described that measures the similarities between input and output HMMs to provide a quality estimate. The correlation between subjective scores and the objective quality measurements are calculated under a variety of conditions to determine algorithm performance. Two different speech datasets are used for testing. Text independence and speaker independence are tested to evaluate the robustness of the algorithm. Experimental results indicate that this new method is robust against distortion and text, while giving fair performance in speaker dependent tests.