  The supersymmetry transformation relating the Konishi operator to its lowest
descendant in the 10 of SU(4) is not manifest in the N=1 formulation of the
theory but rather uses an equation of motion. On the classical level one finds
one operator, the unintegrated chiral superpotential. In the quantum theory
this term receives an admixture by a second operator, the Yang-Mills part of
the Lagrangian. It has long been debated whether this "anomalous" contribution
is affected by higher loop corrections. We present a first principles
calculation at the second non-trivial order in perturbation theory using
supersymmetric dimensional reduction as a regulator and renormalisation by
Z-factors. Singular higher loop corrections to the renormalisation factor of
the Yang-Mills term are required if the conformal properties of two-point
functions are to be met. These singularities take the form determined in
preceding work on rather general grounds. Moreover, we also find non-vanishing
finite terms.
  The core part of the problem is the evaluation of a four-loop two-point
correlator which is accomplished by the Laporta algorithm. Apart from several
examples of the T1 topology with two lines of non-integer dimension we need the
first few orders in the epsilon expansion of three master integrals. The
approach is self-contained in that all the necessary information can be derived
from the power counting finiteness of some integrals.
