[en] The fast vertex search method is suggested for plane geometry. The search for the vertex reduces to comparison of values of the functional in a few easy-to-find points. This method also provides a simple procedure for 'pulling' the vertex to the target. These properties are extremely important for processing the data, obtained in experiments on the search for rare and forbidden decays, when registered events are accidental in most cases. If necessary, the vertex found by this method may be used as an initial approximation for the least square method, which is important for experiments with a big target. The method was examined on three-track events, obtained in the experiment of the search for the forbidden decay μ→3e on the ARES facility. 6 refs.; 6 figs