Existence of a smooth frame for a vector bundle

Question

Let $p:E\rightarrow M$ be a smooth n dimensional bundle and $M$ a smooth manifold. My question is does there always exist a local frame for this vector bundle. A local frame is a collection of smooth sections $r_1,...,r_n:U\rightarrow E$ such that $r_1(m),...,r_n(m) $ is a basis for $p^{-1}(m)$. If such a frame exist how can we find it? Thank you!