The unstable FBS molecule has been produced in the gas phase by a high-temperature reaction between crystalline boron and sulfur tetrafluoride. Its rotational spectrum has been observed in the millimeter-wave region, from 75 to 460 GHz, for different isotopic species and vibrational states. All the excited states which approximately lie below 1700 cm(-1), that are 10(0)0 (F-B stretch), 01(1)0 (FBS bend), 00(0)1 (B=S stretch), 20(0)0, 02(0)0, 02(2)0, 03(1)0, 03(3)0, 04(0)0, 04(2)0, 04(4)0, 11(1)0, 12(0)0, and 12(2)0, have been investigated for the most abundant isotopomer (FBS)-B-11-S-32. The analysis of the spectra has been performed taking simultaneously into account the Fermi interaction which couples the states nu (1),nu (2),nu (3) with nu (1)-1, nu (2)+2,nu (3), and l-type resonances between different sublevels of a given vibrational bending state. This procedure allowed us to calculate directly deperturbed parameters and, in addition, yielded reliable estimates of the vibrational energy difference between the interacting levels and of the normal coordinate cubic force constant k(122). Rotational spectra in the ground and various excited states have been also recorded and analyzed for the less abundant isotopic species (FBS)-B-10-S-32, (FBS)-B-11-S-34, (FBS)-B-10-S-34, (FBS)-B-11-S-33, and (FBS)-B-10-S-33. The very weak spectrum in the 00(0)1 state was successfully observed for the pair of isotopomers (FBS)-B-11-S-32 and (FBS)-B-10-S-32, whose equilibrium rotational constants could be accurately calculated yielding the first evaluation of the equilibrium structure of fluorothioborine: r(e)(F-B)=1.2762 +/-0.0002 Angstrom and r(e)(B=S)=1.6091 +/-0.0002 Angstrom.