The dielectric relaxation of a substituted monohydroxy alcohol, 3-methylthio-1-hexanol, is studied in the highly viscous regime near the glass transition. The Debye relaxation is detected in the dielectric spectra showing the slowest and strongest relaxation dynamics. The calorimetric and dielectric measurements of the liquid and the mixtures with a Debye liquid (2-ethyl-1-hexanol) and a non-Debye liquid (2-ethylhexylamine) reproduce the dynamic characters of the relaxations in monohydroxy alcohols. The Debye relaxation strength and time of 3-methylthio-1-hexanol do not change much compared with 2-ethyl-1-hexanol, while the structural relaxation strength shows a considerable enhancement accompanied by an increase in relaxation time, indicative of a reduction in the dynamic separation between the Debye and structural relaxations. The experimental results allow for the examination of the structural models proposed for the Debye relaxation.