The purpose of this note is to generalize to the topological category the fact that a suitable differentiable manifold is parallelizable (Theorem 4 of [1]). This result has a "folk-theorem" status in some quarters, but I believe that in view of the recent interest in H-manifolds [2], it would be desirable to have the result on record. Let M be an n-manifold. Define A: M--M x M to be the diagonal map, and 7T', 7T2: M x M--M to be the projections on the first and second factor respectively. Milnor [3] calls the diagram A: M;?M x M: Il the tangent microbundle of M, where for each point beM there exists an open set Ub in M containing b, an open set Vb in Mx M containing A(b), and a homeomorphism h: Vb--Ub x Rn such that the following diagram commutes: Ub idxO A lUb Ub x R-< h V