Using the Feynman-Dyson method, the cross section for the creation of an electron pair by a fast charged particle is calculated but in a manner more precise than that of Bhabha and others. The differential cross section obtained here is valid as long as the energies of participant particles are large compared with the respective rest masses. The ambiguities in Bhabha's calculation are also examined. It is concluded that the theoretical value must be compared with the experimental results produced by high energy electrons (≳10 Bev).