The kinetic theory of the electrons in a strongly ionized, collision dominated plasma is reconsidered. By means of a perturbation expansion combined with a multiple time scales formalism, the kinetic equation for the electron distribution function is solved. The usual integro- differential operator is transformed into a pure differential operator. In a fully ionized plasma this operator reduces to a surprisingly simple form when compared to the original one of Spitzer et al. This greatly simplifies the numerical calculation of the transport coefficients.