  We compute the non-planar contribution to the anomalous dimension of the
eight moment of the twist-2 operators in N=4 supersymmetric Yang-Mills theory
at four loops. This result was obtained from the calculations of some elements
of the anomalous dimension matrix for twist-2 operators with the help of a
relations between its elements and eigenvalues. The properties of the obtained
result and a possible relations with a planar results are discussed.
