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In this correspondence, a least mean squares (LMS)-based algorithm is devised for unbiased system identification in the presence of white input and output noise, assuming that the ratio of the noise powers is known. The proposed approach aims to minimize the mean square value of the equation-error function under a constant-norm constraint and is equivalent to minimizing a modified mean square error (MSE) function. An analysis of the algorithm shows that the estimates will converge to the true values in the mean sense. The variances of the parameter estimates are also available. Computer simulations are included to corroborate the theoretical development and to evaluate the impulse response estimation performance of the LMS algorithm under different conditions.