  We study a marginal deformation of N=4 Yang-Mills, with a real deformation
parameter beta. This beta-deformed model has only N=1 supersymmetry and a
U(1)xU(1) flavor symmetry. The introduction of a new superspace star-product
allows us to formulate the theory in N=4 light-cone superspace, despite the
fact that it has only N=1 supersymmetry. We show that this deformed theory is
conformally invariant, in the planar approximation, by proving that its Green
functions are ultra-violet finite to all orders in perturbation theory.
