TITLE: Is the unit tangent bundle of $S^{n}$ parallelizable?
QUESTION [5 upvotes]: Is the unit tangent bundle of $S^{n}$ a  parallelizable  manifold.  This  is motivated by the fact that $TS^{n}$ is parallelizable?

REPLY [12 votes]: W.Sutherland.  A note on the parallelizability of sphere bundles over sphere. J. London Math. Soc. 39 (1964), 55--62. 
The answer is yes.