  In the heavy quark limit, a doubly heavy baryon is regarded as composed of a
heavy diquark and a light quark. We establish the Bethe-Salpeter (BS) equations
for the heavy diquarks and the doubly heavy baryons, respectively, to leading
order in a $1/m_{Q}$ expansion. The BS equations are solved numerically under
the covariant instantaneous approximation with the kernels containing scalar
confinement and one-gluon-exchange terms. The masses for the heavy diquarks and
the doubly heavy baryons are obtained and the non-leptonic decay widths for the
doubly heavy baryons emitting a pseudo-scalar meson are calculated within the
model.
