  We extend the recent result of T.Tao to wave maps defined from the Minkowski
space of dimension >4 to a target Riemannian manifold which possesses a
``bounded parallelizable'' structure. This is the case of Lie groups,
homogeneous spaces as well as the hyperbolic spaces. General compact Riemannian
manifolds can be imbedded as totally geodesic submanifolds in bounded
parallelizable manifolds, and therefore are also covered, in principle, by our
result. Compactness of the target manifold, which seemed to play an important
role in Tao's result, turns out however to play no role in our discussion. Our
proof follows closely that of Tao's recent paper and is based, in particular,
on its remarkable microlocal gauge renormalization idea.
