  This is our second work in the series about constructing boundary conditions
for hyperbolic relaxation approximations. The present work is concerned with
the one-dimensional linearized Jin-Xin relaxation model, a convenient
approximation of hyperbolic conservation laws, with non-characteristic
boundaries. Assume that proper boundary conditions are given for the
conservation laws. We construct boundary conditions for the relaxation model
with the expectation that the resultant initial-boundary-value problems are
approximations to the given conservation laws with the boundary conditions. The
constructed boundary conditions are highly non-unique. Their satisfaction of
the generalized Kreiss condition is analyzed. The compatibility with initial
data is studied. Furthermore, by resorting to a formal asymptotic expansion, we
prove the effectiveness of the approximations.
