We present a Queueing and Markov chain decomposition method based on the total expectation theorem. Our decomposition method requires partial flow to be conserved, which we call a termination scheme. This scheme is useful when deriving analytical formulas for complex queueing systems. As an example, we apply our method to derive an exact set of stationary equations for the probability generating functions of decomposed chains of Markov-modulated continuous-time Markov chains.