  We continue our attempts to systematize baryons, which are composed of light
quarks ($q=u,d$), as quark--diquark systems. The notion of two diquarks is
used: (i) $D^{1}_{1}$, with the spin $S_D=1$ and isospin $I_D=1$ and (ii)
$D^{0}_{0}$, with $S_D=0$ and $I_D=0$. Here we try to resolve the problem of
the low-lying $\Delta(\frac 52^-)$ states: in the last experiments the lightest
state is observed at $\ga 2200$ MeV, not at $1900 - 2000$ MeV as it has been
stated 20 years ago. We are looking for different systematization variants with
the forbidden low-lying $\Delta(\frac 52^-)$ states in the mass region $\la
2000$ MeV. We see that the inclusion of the SU(6) constraints on $qD^{1}_{1}$
states with angular momentum L=1 results in a shift of the lightest
$\Delta(\frac 52^-)$ isobar to $\sim 2300$ MeV. The scheme with the SU(6)
constraints for low-lying $qD^{1}_{1}$ and $qD^{0}_{0}$ states (with $L=0,1$)
is presented in detail here.
