  The differential cross section of double bremsstrahlung from high-energy
electron in the electric field of heavy atoms is derived. The results are
obtained with the exact account of the atomic field by means of the
quasiclassical approximation to the wave functions and the Green's function in
the external field. It is shown that the Coulomb corrections to the
differential cross section (the difference between the exact result and the
result obtained in the leading Born approximation) correspond to small momentum
transfers. The Coulomb corrections to the differential cross section of double
bremsstrahlung are accumulated in the factor, which coincides with the
corresponding factor in the differential cross section of single
bremsstrahlung. At small momentum transfer, this factor is very sensitive to
the parameters of screening while the Coulomb corrections to the spectrum have
the universal form.
