  We revisit the renormalisation group equations (RGE) for general
renormalisable gauge theories at one- and two-loop accuracy. We identify and
correct various mistakes in the literature for the $\beta$-functions of the
dimensionful Lagrangian parameters (the fermion mass, the bilinear and
trilinear scalar couplings) as well as the dimensionless quartic scalar
couplings. There are two sources for these discrepancies. Firstly, the known
expressions for the scalar couplings assume a diagonal wave-function
renormalisation which is not appropriate for models with mixing in the scalar
sector. Secondly, the dimensionful parameters have been derived in the
literature using a dummy field method which we critically re-examine, obtaining
revised expressions for the $\beta$-function of the fermion mass. We perform an
independent cross-check using well-tested supersymmetric RGEs which confirms
our results. The numerical impact of the changes in the $\beta$-function for
the fermion mass terms is illustrated using a toy model with a heavy
vector-like fermion pair coupled to a scalar gauge singlet. Unsurprisingly, the
correction to the running of the fermion mass becomes sizeable for large Yukawa
couplings of the order of O(1). Furthermore, we demonstrate the importance of
the correction to the $\beta$-functions of the scalar quartic couplings using a
general type-III Two-Higgs-Doublet-Model. All the corrected expressions have
been implemented in updated versions of the Mathematica package SARAH and the
Python package PyR@TE.
