Can be a transition matrix of homogeneous Markov's Chain to be disjoint in t?

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Can be a transition matrix of homogeneous Markov's Chain to be discontonuous of $t$, if $P(X_τ = j∣X_{t_n} = i_n, X_{t_n−1} = i_{n−1}, . . . , X_{t_1} = i_1) = P(X_τ = j∣X_{t_n} = i_n)$ $\forall t_1<t_2<...<t_n<\tau$ $\forall i_1, i_2...,i_n, j \in \{1...r\}$?