  We compute the nonplanar contribution to the universal anomalous dimension of
the SU(4)-singlet twist-two operators in N=4 supersymmetric Yang-Mills theory
at four loops through Lorentz spin 18. From this, we numerically evaluate the
nonplanar contribution to the four-loop lightlike cusp anomalous dimension and
derive the transcendental $\zeta_3$ and $\zeta_5$ parts of the universal
anomalous dimension for arbitrary Lorentz spin in analytic form. As for the
lightlike cusp anomalous dimension and the $\zeta_5$ part of the universal
anomalous dimension, we confirm previous results.
