In the standard model the rate of the π0,η,η′ (M) decays is predicted to be extremely small. Therefore, observation of any of these mesons (M) decay into invisible final state would unambiguously signal the presence of new physics. We propose a new experiment to search for the M → invisible decays aiming to probe new physics. Our experiment utilizes high energy hadronic H4 beams from the CERN SPS and the charge exchange reactions of pion on nucleons of an active target, e.g. π− + p → π0 + n, as a source of the well tagged Ms emitted in the forward direction with the beam energy. If the decay M → invisible exists, it could be observed by looking for an excess of events with a specific signature: the complete disappearance of the beam energy in the detector. This unique signal of M → invisible decays allows searches for the π0,η,η′ → invisible decays with the sensitivity few orders of magnitude beyond the present experimental limits. This experiment is complementary to our search for invisible decays of dark photons.