The hypothesis of the rotation of the Local stellar system (LSS) is used to explain the components in the proper motions of stars that the standard kinematic model does not describe. The LSS rotational parameters are derived from the proper motions of the GC reduced onto fundamental systems of the catalogues N30, FK4 and FK5. A weak dependence of the parameters on choice of the fundamental system is found. Some preliminary results are obtained from the radial velocities of the FK5 and the proper motions of the PPM.