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The infrared Fourier transform spectrum of the S-H stretching fundamental band of CH$_{3}$SH at 2604 cm$^{-1}$ has been recorded using synchrotron radiation at the FIR beamline of the Canadian Light Source in Saskatoon. This band is an order of magnitude weaker than the corresponding O-H stretch of methanol, with a very different structure. It is a hybrid band predominantly of perpendicular $b$-type, with a smaller parallel $a$-component. With both $\Delta$$K$ = +1 and $\Delta$$K$ = -1 sub-bands present, the assignments are well-determined from ground-state combination relations, but are complicated by the presence of many $J$-localized perturbations. Upper-state term values have been determined for $K$ = 0-14, and the substate origins have been fitted to a Fourier model. The oscillation amplitude of the torsional curves is 0.545 cm$^{-1}$ compared to 0.652 cm$^{-1}$ for the ground state, indicating a reduction of the order of 16% in the torsional barrier height $V_{3}$.