A base plate for fastening a rail to a fixed bottom support, there being formed in the base plate an opening, which runs from its upper side to its underside, for an eccentric sleeve, which eccentric sleeve is adjustable in rotation in the opening for a sleeve, about an axis of rotation defined by a fastening member inserted through the eccentric sleeve, to allow changes in the position of the base plate. In the opening for the sleeve are markers for indexing for fixing the position in rotation of the eccentric sleeve, the markers spaced from one another such that, an adjustment of the eccentric sleeve in rotation between two adjacent markers for indexing involves a step-by-step change in the position of the base plate by a defined amount.