  We construct a specific formalism for calculating the one-loop virtual
corrections for standard model processes with an arbitrary number of external
legs. The procedure explicitly separates the infrared and ultraviolet
divergences analytically from the finite one-loop contributions, which can then
be evaluated numerically using recursion relations. Using the formalism
outlined in this paper, we are in position to construct the next-to-leading
order corrections to a variety of multi-leg QCD processes such as multi-jet
production and vector-boson(s) plus multi-jet production at hadron colliders.
The final limiting factor on the number of particles will be the available
computer power.
