We study the group structure of baryon anti-decuplet containing the Θ + . We derive the SU(3) mass relations among the pentaquark baryons in the anti-decuplet, when there is either no mixing or ideal mixing with the pentaquark octet, as advocated by Jaffe and Wilczek. This constitutes the Gell-Mann-Okubo mass formula for the pentaquark baryons. We also derive SU(3) symmetric Lagrangian for the interactions of the baryons in the anti-decuplet with the meson octet and the baryon octet. Our analysis for the decay widths of the anti-decuplet states suggests that the N (1710) is ruled out as a pure anti-decuplet state, but it may have anti-decuplet component in its wavefunction if the multiplet is mixed with the pentaquark octet. The recent discovery of the Θ + baryon by LEPS Collaboration at SPring-8 [1], which has been confirmed by several groups [2], initiated a lot of theoretical works in the field of exotic hadrons. Experimentally, the Θ + is observed to have a mass of 1540 MeV and a decay width of < 25 MeV. Because of its positive strangeness, the Θ + baryon is exotic since its minimal quark content should be uudds. Other states that have positive strangeness but different charges are not observed, which suggests that the Θ + is an isosinglet. The existence of such an exotic state with narrow width was first predicted by Diakonov et al. [3] in the chiral soliton model, where the Θ + is a member of the baryon anti-decuplet. Although it should be confirmed by other experiments, the recently discovered Ξ −− 3/2 baryon [4] strongly supports the anti-decuplet nature of pentaquark baryons. The discussion on the existence of a baryon anti-decuplet has a longer history going back to the early 1970's [5], and in the Skyrme model [6]. Pentaquark states with a heavy antiquark (uuddc, uuddb) were also predicted in the Skyrme model. Here an important issue is whether such nonstrange heavy pentaquark states are stable against strong decays [7,8,9,10,11]. Subsequent theoretical investigations on the Θ + include approaches based on the constituent quark model [12,13,14], Skyrme model [15,16,17,18,19], QCD sum rules [20,21], lattice QCD [22], chiral potential model [23], large N c QCD [24], and Group theory approach [25]. The production of the Θ + was also discussed in relativistic nuclear collisions [26], where the number of the anti-Θ + (1540) produced are expected to be similar to that of the Θ + (1540).Several pressing issues that should be clarified are whether the Θ + has positive or negative parity, and whether the Roper N (1710) is included in the baryon anti-decuplet with the Θ + . As for the spin-parity of the Θ + , several works claim that J P = 1 2 − is more natural [13,21,22], which, however, is in contrast to the prediction of the soliton models, where the relative orbital angular momentum plays an important role 10