On the Invalidity of a Conjecture of Dirac

Besed on the symmetry properties of constrained Hamiltonian system, we present one other example to show that Dirac’s conjecture fails in a different way than other examples in that there is no linearization of constraint in this problem. A clear discussion is made on the relationships of the coefficients connecting with the first-class constraints in the gauge generator for a constrained Hamiltonian system. The results of this counterexample are also in contradiction with the other conclusions.