  Fierz transformations for four-fermion operators are generalized to the
one-loop level. A general renormalization scheme is used to compute QCD and QED
corrections to the tree-level relations, which result from Fierz-evanescent
operators. The results can be used to perform general one-loop basis
transformations involving four-fermi and evanescent operators. We illustrate
the usefulness of our results by discussing two examples from a matching
calculation and a one-loop basis change.
