  We analytically compute the four-loop QCD corrections for the colour
structure $(d_F^{abcd})^2$ to the massless non-singlet quark form factor. The
computation involves non-trivial non-planar integral families which have master
integrals in the top sector. We compute the master integrals by introducing a
second mass scale and solving differential equations with respect to the ratio
of the two scales. We present details of our calculational procedure.
Analytical results for the cusp and collinear anomalous dimensions, and the
finite part of the form factor are presented. We also provide analytic results
for all master integrals expanded up to weight eight.
