The edge of the wedge theorem is generalized to the case where one only assumes the existence and equality of the distribution boundary values off ±(z) and all their derivatives on some analytic curveC inR n . Heref ±(z) are holomorphic inR n ±iC, respectively, whereC is a convex cone, andC has its tangent vector inC at every point. Under these assumptions there exists an analytic continuationf(z) holomorphic in some complex neighbourhood of the double cone generated byC. A proof is also given of the connection between the existence of a distribution boundary value and the growth of the holomorphic function near the boundary.