We describe a simple variant of the interpolated Markov model with non-emitting state transitions and prove that it is strictly more powerful than any Markov model. Empirical results demonstrate that the non-emitting model outperforms the interpolated model on the Brown corpus and on the Wall Street Journal under a wide range of experimental conditions. The nonemitting model is also much less prone to overtraining. The remainder of our article consists of four sections. In section 2, we review the interpolated Markov model and briefly demonstrate that all interpolated models are equivalent to some basic Markov model of the same.