A T-dual version of the Gimon-Polchinski orientifold can be described by a configuration of intersecting Dirichlet seven-branes and orientifold seven-planes in the classical limit. We study the modification of this background due to quantum corrections. It is shown that non-perturbative effects split each orientifold plane into a pair of nearly parallel seven-branes, Furthermore, a pair of intersecting orientifold planes, instead of giving rise to two pairs of intersecting seven-branes, gives just one pair of seven-branes, each representing a pair of nearly orthogonal seven-branes smoothly joined to each other near the would-be intersection point. Interpretation of these results from the point of view of the dynamics on a three-brane probe is also discussed. (C) 1997 Published by Elsevier Science B.V.