We derive a set of equations obeyed by the S-matrix of planar N=4 SYM using OPE for Wilson loops. The equations, based on the Yangian symmetry, involve only finite quantities and uniquely determine the all-loop S-matrix. When expanded in powers of the coupling they give derivatives of amplitudes as single integrals over lower-loop ones. We apply them on a few examples, reproducing a recent result on the two-loop NMHV hexagon and fixing previously undermined coefficients in a recent Ansatz for the three-loop MHV hexagon.

AEI, Potsdam