  An experimental study of the production of up-going charged particles in
inelastic interactions of down-going underground muons is reported, using data
obtained from the MACRO detector at the Gran Sasso Laboratory. In a sample of
12.2 10^6 single muons, corresponding to a detector livetime of 1.55 y, 243
events are observed having an up-going particle associated with a down-going
muon. These events are analysed to determine the range and emission angle
distributions of the up-going particle, corrected for detection and
reconstruction efficiency. Measurements of the muon neutrino flux by
underground detectors are often based on the observation of through-going and
stopping muons produced in $\nu_\mu$ interactions in the rock below the
detector. Up-going particles produced by an undetected down-going muon are a
potential background source in these measurements. The implications of this
background for neutrino studies using MACRO are discussed.
