The potential possibilities of the previously proposed method for detecting early reflections, which consists in estimating the excess kurtosis at short intervals of the room impulse response, have been studied. The dependences of detection probability and false alarm probability on segment length were obtained by means of computer simulation. In order to increase the reliability of detecting early reflections, a two-stage algorithm is proposed. At the first stage, the excess kurtosis is measured within the segments of the impulse response, and the maxima of those segments where the excess kurtosis estimate exceeds a given threshold are selected. The procedure for selecting maxima is repeated several times for segments of different lengths. As a result, a set of moments of time is formed, which pretend to be the reflection onset timings. At the second stage, a histogram of the distribution of these moments is constructed. The decision about the presence of early reflections is made using this histogram. The performance of the proposed algorithm was experimentally verified using binaural impulse characteristics of a real room. It was shown that the reflection onset timing measuring error did not exceed 0.1 ms in 80% of cases.