  We compute the partition function for the exotic instanton system
corresponding to D-instantons on D7 branes in Type I' theory. We exploit the
BRST structure of the moduli action and its deformation by RR background to
fully localize the integration. The resulting prepotential describes
non-perturbative corrections to the quartic couplings of the gauge field F
living on the D7's. The results match perfectly those obtained in the dual
heterotic theory from a protected 1-loop computation, thus providing a
non-trivial test of the duality itself.
