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In this paper we propose a new technique for estimating the center frequency of the ultrasound pulse from records of backscattering noise. We start by considering that the conventional maximum frequency method can be seen as a filtering (differentiator) of the pulse spectrum magnitude followed by a searching for the zero-crossing value. The new approach replaces the differentiator by a Hilbert transformer. We show in the paper that the proposed method has less variance than the maximum frequency method. In particular, we analyse the performance assuming that the real cepstrum method is used for extracting pulse spectrum magnitude. We give an upper bound for the variance reduction when practical criteria are applied for fitting the cepstrum cut-off frequency. The analytical work is verified by real and simulated data.