  We investigate the spin 3/2 baryons in the 27-plet based on flavor SU(3)
symmetry. For $J^p=3/2^+$, we find all the candidates for non-exotic members.
For $J^p=3/2^-$, we predict a new non-exotic member $\Lambda(1780)$. Fitting
the mass spectrum and calculating the widths of the members show an approximate
symmetry of the 27-plet of SU(3). We find that the exotic members have
relatively large widths and the $\Xi(1950)$ has spin and parity $J^p=3/2^-$.
The possibility of assigning the non-exotic candidates to an octet is also
analyzed.
