  The remainder function of Wilson loops for null polygons becomes divergent if
two vertices approach each other. We apply RG techniques to the limiting
configuration of a contour with self-intersection. As a result for the two loop
remainder we find a quadratic divergence in the logarithm of the distance
between the two approaching vertices. The divergence is multiplied by a factor,
which is given by a pure number plus the product of two logarithms of
cross-ratios characterising the conformal geometry of the self-crossing.
