Are all vector bundles “flat vector bundles”?

This concept appears in Bott&Tu's GTM82. A flat vector bundle is one who has a particular trivialization with locally constant transition functions. Then my question is whether every vector bundle over a manifold admits such a trivialization.

btw: Are the tags correct?

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In particular, the tangent bundle of $S^2$ can't be given a flat structure. –  Ryan Budney Oct 20 '11 at 4:05