  Using a Mellin-Barnes representation, we compute the on-shell massless planar
double box Feynman diagram with an irreducible scalar product of loop momenta
in the numerator. This diagram is needed in calculations of two loop
corrections to scattering processes of massless particles, together with the
double box without numerator calculated previously by Smirnov. We verify the
poles in epsilon of our result by means of a system of differential equations
relating the two diagrams, which we present in an explicit form. We verify the
finite part with an independent numerical check.
