We present a new stopping criterion for the matching pursuit (MP) algorithm, based on evaluating stationarity of the residua of the consecutive MP iterations. The new stopping criterion is based on a model of a nonstationary signal, which assumes that the part of the signal that is of interest is nonstationary and contaminated by a weakly stationary noise. Mean- and variance-stationarity of the residua obtained from each step of MP is evaluated by means of dedicated statistical tests-the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test and the White test, respectively. We illustrate the proposed concept by an example in which we analyse magnetoencephalographic (MEG) data.