  The way of finding all the constraints in the Hamiltonian formulation of
singular (in particular, gauge) theories is called the Dirac procedure. The
constraints are naturally classified according to the correspondig stages of
this procedure. On the other hand, it is convenient to reorganize the
constraints such that they are explicitly decomposed into the first-class and
second-class constraints. We discuss the reorganization of the constraints into
the first- and second-class constraints that is consistent with the Dirac
procedure, i.e., that does not violate the decomposition of the constraints
according to the stages of the Dirac procedure. The possibility of such a
reorganization is important for the study of gauge symmetries in the Lagrangian
and Hamiltonian formulations.
