For an orientable compact manifold $M$ with boundary, is its boudary orientable as well?

If $M$ is smooth, the conclusion obviously holds. For the general manifold, my plan is to use long exact sequence $H_n(M,\partial M)\rightarrow H_{n-1}(\partial M) $ to show the latter homology group is $\mathbb Z$, but I stuck there.

Topology and Geometry, or Dold's lecture on algebraic topology. – Liviu Nicolaescu Jul 31 '12 at 8:48