We present a theoretical study of the internal rotation of HSOH. Calculations at the ab initio HF//6-311G** level show that HSOH is a gauche molecule presenting a double-barrier torsional potential. The different mechanisms associated with isomerization passing by a trans or a cis barrier have been characterized with the use of the profiles of potential energy (V), electronic chemical potential (mu), and molecular hardness (eta). Important results have been obtained : (a) the principle of maximum hardness is verified; (b) the profiles of mu and eta in connection with that of local electronic populations allows one a qualitative characterization of the nature of the two potential barriers hindering the internal rotation.