  We derive an upper bound on the mass difference between the $\Xi^*$ and
$\Theta^+$ pentaquarks which are the manifestly exotic members of the $SU(3)_f$
antidecuplet. The derivation is based on simple assumptions about $SU(3)_f$
symmetry breaking and uses the standard quantum mechanical variational method.
The resulting rather robust bound is more than 20 MeV below the experimentally
reported $\Xi^*-\Theta^+$ mass difference, emphasizing the need for
confirmation of the experimental mass values and placing strong constraints on
quark models of the pentaquark structure.
