The cross section for high energy muon bremsstrahlung on heavy atoms i
s calculated without the use of the Born approximation. It is shown th
at the correction to the Born approximation in the region of momentum
transfers q of the order of mu c has the same order of magnitude as th
e well-known correction of Davies, Bethe, and Maximon. It is shown als
o that these corrections have different signs and nearly compensate ea
ch other.