  We investigate the symmetry property and construct the wave function of the
dibaryon states containing two strange quarks with S=0 in both the flavor SU(3)
symmetric and breaking cases. We discuss how the color $\otimes$ isospin
$\otimes$ spin states of dibaryon in the symmetry broking case of flavor SU(3)
can be extracted from the fully antisymmetric states in flavor SU(3). The
stability of the dibaryon against the strong decay into two baryons are then
discussed, by using the variational method within a constituent quark model
with a confining and color-spin interactions. To compare our results with that
from lattice QCD in flavor SU(3) limit, we search for the stable H-dibaryon in
a wide range of $\pi$ meson mass. We find that with the given potential, there
is no compact six quark dibaryon state in the SU(3) flavor symmetry broken case
with realistic quark masses as well as in flavor SU(3) symmetric case in a wide
range of quark masses.
