This paper shows that the HMM whose state output vector includes static and dynamic feature parameters can be reformulated as a trajectory model by imposing the explicit relationship between the static and dynamic features. The derived model, named trajectory HMM, can alleviate the limitations of HMMs: i) constant statistics within an HMM state and ii) independence assumption of state output probabilities. We also derive a Viterbi-type training algorithm for the trajectory HMM. A preliminary speech recognition experiment based on N-best rescoring demonstrates that the training algorithm can improve the recognition performance significantly even though the trajectory HMM has the same parameterization as the standard HMM.