  We manifest the origin of the wrong conclusion made by several groups of
authors on the absence of Coulomb corrections to the cross section of the
e^+e^- pair production in ultrarelativistic heavy-ion collisions. The source of
the mistake is connected with an incorrect passage to the limit in the
expression for the cross section. When this error is eliminated, the Coulomb
corrections do not vanish and agree with the results obtained within the
Weizs\"acker-Williams approximation.
