  We have measured directly the residual energy of cosmic ray muons crossing
the MACRO detector at the Gran Sasso Laboratory. For this measurement we have
used a transition radiation detector consisting of three identical modules,
each of about 12 m^2 area, operating in the energy region from 100 GeV to 1
TeV. The results presented here were obtained with the first module collecting
data for more than two years. The average single muon energy is found to be 320
+/- 4 (stat.) +/- 11 (syst.) GeV in the rock depth range 3000-6500 hg/cm^2. The
results are in agreement with calculations of the energy loss of muons in the
rock above the detector.
