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This paper presents an auxiliary model based stochastic gradient parameter estimation algorithm for multi-input output-error systems by minimizing a quadratic cost function. The basic idea is to replace the unknown variables in the information vector with the outputs of an auxiliary model or estimated outputs and the analysis and simulation results indicate that the parameter estimates converge to their true values for persistent excitation input signals. The algorithm proposed has significant computational advantage over existing least squares identification algorithms. A simulation example is given.