this paper derives extended three-stage recursive identification algorithm of MISO for (CARARMA) systems. Based on The decomposition technique, four subsystems are obtained and the parameters of each subsystem are identified. Some model validation methods are computed to measure the model value and Akaike's Final Prediction Error Criterion (FPE) is used to verify the selection of system order. The algorithm has a high computational efficiency because the covariance matrices dimensions become small in each subsystem. Finally, this algorithm effectiveness is demonstrated in simulation example.