Let [Formula: see text] be a locally compact abelian (LCA) group and [Formula: see text] be a topological automorphism on [Formula: see text]. For [Formula: see text], the Stockwell transform on the locally compact group [Formula: see text] with respect to the automorphism [Formula: see text] is defined and denoted by [Formula: see text]. The inversion formula for the Stockwell transform [Formula: see text] is established and as a result it is concluded that [Formula: see text] is an isometry. Moreover, some properties of the Stockwell transform [Formula: see text] are examined. Finally, some examples are given to support our technical considerations.