We know that the middle circle $S^1$ in Mobius band has a nontrivial normal bundle. Now consider the higher dimensional case. Let $M$ be a $n$-dimensional ($n\geq5$) closed orientable manifold and some $S^2$ is embedded in $M$.

Does $S^2$ always have a trivial normal bundle in $M$?

If the answer is 'No', what conditions on $M$ can make sure the answer is 'yes'? Spin manifolds? In surgery theory, we always want an embedding of $S^k \times D^{n-k}$ in $M$ to do surgery and the trivial normal bundle is necessary. Any references or comments are welcomed.