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The paper deals with the wavelet transform potential for localization of leakages in the pumping complex pipeline network. The relationship of wave processes in the head signals and the change of the wavelet coefficients in the time and frequency domain are determined. It is proved that the beginning of the emergency mode corresponds to the first abrupt change in the root-mean-square values of the wavelet coefficients in the head signal. To identify the coordinate of the leakage in the pipeline network it is proposed to use the time moments of the first abrupt change of the root-mean-square values of the wavelet coefficients. It is found that the error of determining the location of a leakage is affected by the geometry of the pipeline, the speed of the shock wave propagation, the type of the leakage and its volume. The obtained theoretical results are confirmed experimentally in a pumping complex laboratory setup.