  It is shown that an arbitrary singular Lagrangian theory (with first and
second class constraints up to $N$-th stage in the Hamiltonian formulation) can
be reformulated as a theory with at most third-stage constraints. The
corresponding Lagrangian $\tilde L$ can be obtained by pure algebraic methods,
its manifest form in terms of quantities of the initial formulation is found.
Local symmetries of $\tilde L$ are obtained in closed form. All the first class
constraints of the initial Lagrangian turn out to be gauge symmetry generators
for $\tilde L$.
