We report on a direct search for a three-body decay of the orthopositronium into a photon and two penetrating particles, o-Ps→ γ+X 1+X 2. The existence of this decay could explain the discrepancy between the measured and the predicted values of the orthopositronium decay rate. From the analysis of the collected data a single candidate event is found, consistent with the expected background. This allows to set an upper limit on the branching ratio B(o-Ps→ γ+X 1+X 2)<4.4×10 -5 (at the 90% confidence level), for the photon energy in the range from 40 keV < Eγ< 400 keV and for mass values in the kinematical range 0⩽ mX 1+ mX 2⩽900 keV. This result unambiguously excludes the o-Ps→ γ+X 1+X 2 decay mode as the origin of the discrepancy.