  The weak decays Xi_b -> Lambda_b pi and Xi_c -> Lambda_c pi, in which the
heavy quark is not destroyed, are discussed. The branching fractions for these
decays, corresponding to an absolute rate of order 0.01 ps^{-1}, should be at a
one percent level for the b hyperons and at a (few) per mill level for Xi_c,
possibly making feasible their experimental study in future. It is shown,
through an application of the heavy quark limit, the flavor SU(3) symmetry, and
PCAC, that the Delta I = 1/2 rule should hold very well in these decays, and
also that the Xi_b decays are purely S wave in the symmetry limit, while the
difference between the $S$ wave amplitudes of the Xi_c decays and those for the
Xi_b is related, in terms of the heavy quark expansion, to the difference of
the total decay rates within the (Xi_c, Lambda_c) triplet of charmed hyperons.
We also comment on the amplitudes of the semileptonic transitions Xi_Q ->
Lambda_Q l nu and on the weak radiative decays Xi_Q -> Lambda_Q gamma.
