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Abstract This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the decomposition technique and the auxiliary model identification idea, we derive a decomposition based auxiliary model recursive generalized least squares algorithm. The key is to divide the system into two fictitious subsystems, the one including a parameter vector and the other including a parameter matrix, and to estimate the two subsystems using the recursive least squares method, respectively. Compared with the auxiliary model based recursive generalized least squares algorithm, the proposed algorithm has less computational burden. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]