  We study in the Hamiltonian framework the local transformations
$\delta_\epsilon q^A(\tau)=\sum^{[k]}_{k=0}\partial^k_\tau\epsilon^a{}
R_{(k)a}{}^A(q^B, \dot q^C)$ which leave invariant the Lagrangian action:
$\delta_\epsilon S=div$. Manifest form of the symmetry and the corresponding
Noether identities is obtained in the first order formalism as well as in the
Hamiltonian one. The identities has very simple form and interpretation in the
Hamiltonian framework. Part of them allows one to express the symmetry
generators which correspond to the primarily expressible velocities through the
remaining one. Other part of the identities allows one to select subsystem of
constraints with a special structure from the complete constraint system. It
means, in particular, that the above written symmetry implies an appearance of
the Hamiltonian constraints up to at least $([k]+1)$ stage. It is proved also
that the Hamiltonian symmetries can always be presented in the form of
canonical transformation for the phase space variables. Manifest form of the
resulting generating function is obtained.
