  Using the color-magnetic interaction Hamiltonian with SU(3) flavor symmetry
breaking, we perform a schematic study of the masses of the $J^P=1^+$
tetraquarks in the anti-decuplet representation. After diagonalizing the mass
matrix, we find the $ud\bar s\bar s$ tetraquark lies around 1347 MeV. It decays
into $K^+K^0\pi^0, K^+K^+\pi^-, K^0K^0\pi^+$ via P-wave. The dual suppression
from the not-so-big three-body phase space and P-wave decay barrier may render
this exotic state rather narrow. Future experimental exclusion of this state
will cast doubt on the validity of applying the simple color-magnetic
Hamiltonian to the multiquark system.
