Gauge Conditions in the Singular Systems

In terms of the Dirac's finite contact transformation, we derive the principle on the choice of gauge conditions in the general singular Lagrangian system. It is applied successfully to Cawley's first counter-example of Dirac's conjecture. The number of gauge conditions or gauge freedoms is given and it is shown to be different from the accustomed conclusion which is always equal to the number of all the first-class constraints .