  We calculate the two-loop matching corrections for the gauge couplings at the
Grand Unification scale in a general framework that aims at making as few
assumptions on the underlying Grand Unified Theory (GUT) as possible. In this
paper we present an intermediate result that is general enough to be applied to
the Georgi-Glashow SU(5) as a "toy model". The numerical effects in this theory
are found to be larger than the current experimental uncertainty on $alpha_s$.
Furthermore, we give many technical details regarding renormalization
procedure, tadpole terms, gauge fixing and the treatment of group theory
factors, which is useful preparative work for the extension of the calculation
to supersymmetric GUTs.
