  Using Lorentz covariant spinor helicity formalism we reorganize the unitary
scalar superfield light-cone path integral for the N=4 supersymmetric
Yang-Mills theory. In new variables in the chiral Fourier superspace the
quadratic and cubic parts of the classical action have manifest Lorentz,
kinematical and dynamical supersymmetry, with the exception of terms which
contribute only to the contact terms in the supergraphs with propagators
shrinking to a point. These terms have the same structure as supergraphs with
quartic light-cone vertices, which break dynamical supersymmetry. We present
evidence that all complicated terms breaking dynamical supersymmetry have to
cancel and therefore can be omitted. It is plausible that the new form of the
path integral leads to a set of relatively simple unitarity based rules with
manifest N=4 supersymmetry.
