We investigate the axial-vector transition constants of the baryon antidecuplet to the octet and decuplet within the framework of the self-consistent SU(3) chiral quark-soliton model. Taking into account rotational 1/N c and linear m s corrections and using the symmetry-conserving quantization, we calculate the axial-vector transition constants. It is found that the leading-order contributions are generally almost canceled by the rotational 1/N c corrections. Thus, the m s corrections turn out to be essential contributions to the axial-vector constants. The decay width of the Θ + → N K transition is determined to be Γ(Θ → N K) = 0.71 MeV, based on the result of the axialvector transition constant g * A (Θ → N K) = 0.05. In addition, other strong decays of the baryon antidecuplet are investigated.Since the LEPS collaboration announced the evidence of the Θ + existence [1], which was motivated by Ref. [2] where its decay width was predicted to be very small with its mass 1540 MeV [3] as well, there has been a great deal of experimental and theoretical work on the Θ + (see, for example, reviews [4,5] for the experimental and theoretical status before 2006). However, a series of very recent experiments conducted by the CLAS collaboration reported null results of finding the Θ + [6,7,8,9] in various reactions. These CLAS experiments were dedicated ones with high statistics. The null results of the CLAS experiment imply that the total cross sections for photoproductions of the Θ + are tiny. In fact, the 95% CL upper limits on the total production cross sections for the Θ + at 1540 MeV lie mostly in the range of of 0.3 − 0.8 nb [6,7,9]. In Ref.[8] the 95 % CL upper limit on the γd → ΛΘ + total cross section is set to be 5 nb in the mass range between 1.52 and 1.56 GeV/c 2 . The KEK-PS E522 collaboration [10] has performed the experiment searching for the Θ + in the π − p → K − X reaction and found a bump at 1530 MeV/c 2 but with only (2.5 − 2.7) σ statistical significance. The upper limit of Θ + production cross section in the π − p → K − Θ + reaction was extracted to be 3.9µb. A later sequential experiment at KEK, however, has observed no clear peak structure in the K + p → π + X reaction [11], giving a 95 % CL upper limit of 3.5 µb/sr on the differential cross section averaged over 2 • to 22 • .In the meanwhile, the DIANA collaboration has continued to search for the Θ + in the K + n → K 0 p reaction and has found a direct formation of a narrow pK 0 peak with mass of 1537 ± 2 MeV/c 2 and width of Γ = 0.36 ± 0.11 MeV [12]. Note that the former measurement by the DIANA collaboration for the Θ + has yielded the mass of the Θ + 1539 ± 2 MeV/c 2 with the decay width Γ ≤ 9 MeV [13]. The SVD experiment has also announced a narrow peak with the mass M = 1523 ± 2(stat.) ± 3(syst.) MeV/c 2 in the inclusive reaction pA → pK 0 s + X [14,15]. The LEPS collaboration also brings about positive new results indicating the existence of the Θ + [16,17].Theoretically, it is of great importance to understand why the Θ + is rather elusive....