We compute the one-loop four-point function in N = 4 supersymmetric Yang-Mi
lls theory with gauge group U(N). We perform the calculation in N = 1 super
space using the background field method and obtain the complete off-shell c
ontributions to the effective action from planar and non-planar supergraphs
. In the low-energy approximation the result simplifies and we can study it
s properties under gauge transformations. It appears that the non-planar co
ntributions do not maintain the gauge invariance of the classical action.