The present paper is devoted to constructing a hierarchy of relativistic kinematically nonrotating reference systems. The hierarchy includes a barycentic reference system (BRS), a geocentric reference system (GRS), an observer's reference system (ORS). The metric tensor of the ORS as well as the transformation between the GRS and the ORS are expressed in closed form. The spatial rotation of the ORS with regard to the BRS resulting from two subsequent Lorentz transformations (BRS-GRS and GRS-ORS) is discussed. An attempt to clarify the notion of a kinematically nonrotating reference system is undertaken.