  We consider the Coulomb correction (CC) to the $e^+e^-$ pair production
related to multiphoton exchange of the produced $e^{\pm}$ with nuclei. The
contribution of CC to the energy distribution of $e^+$ and $e^-$ as well as to
the total pair production cross section are calculated with an accuracy of the
order of 1%. The found correction to the total Born cross section is negative
and equal to -25% at the RHIC for Au--Au and -14% at the LHC for Pb--Pb
collisions.
