  In this paper we discuss the refined analytic torsion on an odd dimensional
compact oriented Riemannian manifold with boundary under some assumption. For
this purpose we introduce two boundary conditions which are complementary to
each other and well-posed for the odd signature operator $\mathcal{B}$ in the
sense of Seeley. We then show that the zeta-determinants of $\mathcal{B}^2$ and
eta-invariants of $\mathcal{B}$ subject to these boundary conditions are well
defined by using the method of the asymptotic expansions of the traces of the
heat kernels. We use these facts to define the refined analytic torsion on a
compact manifold with boundary and show that it is invariant on the change of
metrics in the interior of the manifold. We finally describe the refined
analytic torsion under these boundary conditions as an element of the
determinant line.
