  The one loop vertex in QED is calculated in arbitrary covariant gauges as an
analytic function of its momenta. The vertex is decomposed into a longitudinal
part, that is fully responsible for ensuring the Ward and Ward-Takahashi
identities are satisfied, and a transverse part. The transverse part is
decomposed into 8 independent components each being separately free of
kinematic singularities in $\bf any$ covariant gauge in a basis that modifies
that proposed by Ball and Chiu. Analytic expressions for all 11 components of
the ${O(\alpha)}$ vertex are given explicitly in terms of elementary functions
and one Spence function. These results greatly simplify in particular kinematic
regimes.
