Transition matrix in left-right hidden semi-Markov model

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I'm developing a hidden semi-Markov model left-right . In a left-right model a sequence of $M$ states starts in state $1$ and ends in state $M$, with no repetition of states. Since the model is semi-Markovian a self transition $a_{ii}=0$ is not allowed. I think the last row of the matrix should be $0$, but the rule is $\sum_{j}a_{ij}=1$. How can I solve this problem?