We give general intersecting brane solutions without assuming any restriction on the metric in supergravity coupled to a dilaton and antisymmetric tensor fields in arbitrary dimensions D. The result is a general class of intersecting brane solutions which interpolate the non-extreme solutions of type 1 and 2. We also discuss the relation of our solutions to the known single brane solution. (C) 2004 Elsevier B.V. All rights reserved.