<p>Currently, a generally accepted and widely used property of multiparticle amplitudes is the absence of simultaneous amplitude discontinuities on energy invariants of overlapping channels. The Steinmann relations are used to substantiate this property. The paper shows the presence of such discontinuities and the illegality of using the Steinmann relations to prove their absence. The existence of discontinuities means that the currently accepted form of multi-Regge amplitudes is erroneous and it should be taken into account when deriving the BFKL (Balitsky–Fadin–Kuraev–Lipatov) equation in the following approximations.</p>