OBJECTIVES: Health economic models typically follow a Markovian framework with discrete health states. The transition probability matrix (TPM), which characterizes the health state transitions, is the key driver of such a model. Estimation of TPM depends upon the observation intervals of clinical studies and the model cycle length. Generally Maximum-Likelihood (ML) or eigen-decomposition method can be used to estimate the TPM. However, these methods are not feasible for studies with non-uniform observation intervals (e.g., observations taken at 1, 3 & 6 months), or when eigenvalues are negative or complex. The current objective is to provide a generalized algorithm to estimate TPM in all possible situations using all the available data.  METHODS: Craig & Sendi (2002) illustrated an EM algorithm approach to estimate 1 month TPM for a 3-state model, where 1 and 2 month observations were available. We generalized this procedure and created an algorithm for any observation intervals and any number of states. We evaluated this algorithm in the following situations: i) Observations at multiple intervals to estimate a single cycle TPM, ii) Seventh month observed transitions to estimate a 2-month TPM when the eigenvalues are complex, iii) Sixth month observed transitions to estimate a 2-month TPM when the eigenvalues are negative.  RESULTS: The generalized EM algorithm approach replicated results obtained from ML and eigen-decomposition method. In cases where eigenvalues were negative and complex, this method provided solutions which were valid and interpretable. In all three situations mentioned above, the generalized EM algorithm produced consistent and valid results.  CONCLUSIONS: A generalized EM algorithm can be a useful tool to estimate TPM, in complex situations where ML estimation and eigen-decomposition cannot be used. It allows the use of all the observed data to estimate the TPM, thus increasing the accuracy of the health economic models.