  We report on a direct search for a three-body decay of the orthopositronium
into a photon and two penetrating particles, o-Ps -> gamma + X1 + X2. 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 <
4.4 \times 10^{-5} (at the 90% confidence level), for the photon energy in the
range from 40 keV < E_gamma< 400 keV and for mass values in the kinematical
range 0 < mX1+mX2 <900 keV. This result unambiguously excludes the o-Ps ->
gamma + X1 + X2 decay mode as the origin of the discrepancy.
