We reconsider the problem of finding all local symmetries of a Lagrangian.
Out approach is completely Hamiltonian without any reference to the associa
ted action. We show that the restrictions on the gauge parameters entering
in the definition of the generator of gauge transformations follow from the
commutativity of a general gauge variation with the time derivative operat
ion. (C) 1999 Elsevier Science B.V. All rights reserved.