A new procedure for computing stationary probabilities for an overloaded Markovian model is proposed interms of the rotated Markov chain.There are two advantages to use this procedure:i) This procedure allows us to approximate an overloaded finite model by using a stable infinite Markov chain. This will makethe study easier when the infinite model has a simpler solution.ii) Numerically, this procedure often significantly reduces the number of computations and the requirement of computer memory. By using different examples,we specifically demonstratethe process of implementing this rotating procedure.