  We analyze a singular theory with first class constraints of an arbitrary
stage. Relation among the formulations of the constrained system in terms of
complete and extended Hamiltonians is clarified. We replace the extended
Hamiltonian $H_{ext}$ by an improved one. The improved Hamiltonian has the same
structure as $H_{ext}$ (higher stage constraints enter into the Hamiltonian in
the manifest form), but, in contrast to $H_{ext}$, it arises as the complete
Hamiltonian for some Lagrangian $\tilde L$, called the extended Lagrangian.
This implies, in particular, that all the quantities appearing in the improved
Hamiltonian have a clear meaning in the Dirac framework. $\tilde L$ is obtained
in a closed form in terms of quantities of the initial formulation $L$. The
formulations with $L$ and $\tilde L$ turn out to be equivalent. As an
application of the formalism, we found local symmetries of $\tilde L$ in a
closed form. All the constraints of $L$ turn out to be gauge symmetry
generators for $\tilde L$. The procedure is illustrated with an example of a
model with fourth-stage constraints.
