This paper proposes a method of improving the accuracy of the attenuation constant estimate obtained by using the cross-spectral technique. In the cross-spectral technique, the envelope of the estimated impulse response is deformed due to the use of a time window. As a result, the estimated impulse response decays more rapidly than the real impulse response does, and the attenuation constant obtained by the estimated impulse response becomes larger than the real value. This paper first describes how the attenuation constant changes in the process of impulse response estimation. Next, we propose a method of improving the accuracy of the estimation. The effect of the proposed method is confirmed by computer simulation.