[en] Highly excited (4.10 <= mass <= 5.35 GeV/c²) four-baryon resonances have been searched for in the missing-mass spectrum of the reaction π^- + ⁴He → π^- + X at 5 GeV/c in the region of small four-momentum transfer (0.005 <= vertical stroke t vertical stroke <= 0.15 (GeV/c)²), where one of the decay products of the X is either proton or deuteron or triton. No resonance signal is seen in the mass spectrum of X. Within our limited acceptance, the cross section for the production of a narrow (GAMMA approx. 20 MeV/c²) four-baryon state with mass 4.9 GeV/c² is estimated to be smaller than approx. 100 nb. (orig.)