  In this paper we analyse formulas which reproduce different contributions to
scattering amplitudes in N=4 super Yang-Mills theory through a Grassmannian
integral. Recently their Yangian invariance has been proved directly by using
the explicit expression of the Yangian level-one generators. The specific
cyclic structure of the form integrated over the Grassmannian enters in a
crucial way in demonstrating the symmetry. Here we show that the Yangian
symmetry fixes this structure uniquely.
