  For a theory with first and second class constraints, we propose a procedure
for conversion of second class constraints based on deformation the structure
of local symmetries of the Lagrangian formulation. It does not require
extension or reduction of configuration space of the theory. We give examples
in which the initial formulation implies a non linear realization of some
global symmetries, therefore is not convenient. The conversion reveals hidden
symmetry presented in the theory. The extra gauge freedom of conversed version
is used to search for a parameterization which linearizes the equations of
motion. We apply the above procedure to membrane theory (in the formulation
with world-volume metric). In the resulting version, all the metric components
are gauge degrees of freedom. The above procedure works also in a theory with
only second class constraints presented. As an examples, we discuss arbitrary
dynamical system of classical mechanics subject to kinematic constraints,
O(N)-invariant nonlinear sigma-model, and the theory of massive vector field
with Maxwell-Proca Lagrangian.
