In this paper we give a short note. A dynamical system of classical mechanics subject to a constraint whose motion may be described in terms of non'inde. pondent generalized coordinates. Suppose the action integral of the system and constraint conditions are invariant under the Symmetry transformations of these generalized Coordinates. Then. For the holonomic Constraint. The Symmetry transformations yield the same results. as Classical Noethers theorem For the linear non-holonomic system. The symmetry transformations ingene. ral do not yield the Conservation laws as Classical Noethers theorem.