  We resolve the SU(3) outer multiplicity problem by defining all possible
$SU(3)\otimes SU(3)$ invariant operators in terms of SU(3) Schwinger bosons. We
show that the elementary invariant operators relevant to the outer multiplicity
problem form SO(4,2) algebra. Further, they enable us to construct a family of
operators any one of which can be used to distinguish repeating representations
present in the reduction of the direct product of two SU(3) irreducible
representations.
