  We propose that the Baxter $Q$-operator for the spin-1/2 XXZ quantum spin
chain is given by the $j\to \infty$ limit of the transfer matrix with spin-$j$
(i.e., $(2j+1)$-dimensional) auxiliary space. Applying this observation to the
open chain with general (nondiagonal) integrable boundary terms, we obtain from
the fusion hierarchy the $T$-$Q$ relation for {\it generic} values (i.e. not
roots of unity) of the bulk anisotropy parameter. We use this relation to
determine the Bethe Ansatz solution of the eigenvalues of the fundamental
transfer matrix. This approach is complementary to the one used recently to
solve the same model for the roots of unity case.
