We construct an explicit supergravity solution for a configuration of localized D4-brane ending on a D6-brane, restricted to the near horizon region of the latter. We generate this solution by dimensionally reducing the supergravity solution for a flat M5-brane in R^1,7 × C²/Z_N with the M5-brane partially embedded in C²/Z_N. We describe the general class of localized intersections and overlaps whose supergravity solutions are constructible in this way.