Generators of the algebra of first class functions in a system with second
class constraints are found. It is shown that first class functions form
algebras with respect to the Dirac bracket and pointwise multiplication.The
subspace of functions vanishing on constraint surface are ideals of these
algebras. The corresponding quotient algebras are isomorphic to the algebras of
phase variables in the Dirac bracket formalism. Explicite expressions for
generators and brackets of the algebras under consideration are obtained.