  In this paper we give all the details of the calculation that we presented in
our previous paper arXiv:0712.3522, concerning the four-loop anomalous
dimension of the Konishi descendant tr(\phi Z\phi Z-\phi \phi Z Z) in the SU(2)
sector of the N=4 planar SYM theory. We explicitly consider all the wrapping
diagrams that we compute using an N=1 superspace approach and Gegenbauer
polynomial x-space techniques.
