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In this correspondence, based on an alternative derivation of the Pisarenko harmonic decomposition (PHD) method, a new asymptotically unbiased estimator for the frequency of a single real tone in white noise is devised with the use of novel sample covariance expressions. Furthermore, extension to sample covariances with higher lags for performance enhancement is investigated while a simple and effective scheme is suggested to resolve the corresponding frequency ambiguity problem. The variance of the modified Pisarenko's method is also derived, which is then utilized to find the best estimate among all admissible solutions from various sets of sample covariances. Computer simulations are included to corroborate the theoretical development and to demonstrate that the proposed approach outperforms several existing low-complexity frequency estimators in terms of nearly uniform performance and estimation accuracy.