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In this article, we propose an improved class of estimators for a finite population variance in presence of the auxiliary information. The expressions of the bias and mean squared error of the proposed class of estimators are obtained up to the first order of approximation. The conditions under which the proposed class of estimators is more efficient than the other estimators have also been derived. It is observed from the simulation results that the proposed class of estimators is more efficient than the usual linear regression estimator.