  We calculate the coupling constant and decay width of the decuplet to octet
baryon transitions in lattice QCD using the transfer matrix method. The
transition amplitude is related to the coupling constant and via the Fermi's
Golden Rule to the decay width. The method is applicable for near-degeneracy of
the energy levels of initial and final states and, when this condition is
fulfilled, yields a good estimate of the decay width. We present results using
a hybrid action with domain wall valence quarks on a staggered sea with $350$
MeV pion mass as well as for a domain wall fermion action with $180$ MeV pion
mass. We find $\Gamma\left( \Delta \to \pi\,N \right) = 119\,( 8)\,( 8)$ MeV
for the transition of Delta to pion-nucleon within the unitary domain wall
setup. We also report values for the decay widths of the $\Sigma^*$ and $\Xi*$
baryons.
