Reconstruction of higher-stage first-class constraints into the secondary ones

Starting from a Lagrangian theory L with first class constraints up to Nth stage, we construct an equivalent Lagrangian (L) over tilde L with at most secondary first-class constraints presented in a Hamiltonian formulation. The Lagrangian (L) over 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 (L) over tilde L are found in a closed form. All the constraints of L turn out to be gauge symmetry generators for (L) over tilde L.