The main purpose of the paper is to prove that the map (7) and also its restriction to GL+ (n, IR) is a locaily trivial fibration. From the general theory of fiber bundles we know th a t a bu.ndle map between two C “ -differentiable manifolds is a surjeetive submersion. Here arise a natural problem: given M and N two C00— differentiable manifolds and f: M -> N a smooth surjeetive submersion, find suffi- cient conditions in order th a t f be a locaily trivial fibration. A such condition is given by: