An inherent ambiguity of broken $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ symmetry is discussed. It is shown to arise from a discrete unitary transformation in the $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ space. For Hamiltonian models for which the symmetry-breaking term transforms like the $(3,\overline{3})+(\overline{3},3)$ representation, we find that, in general, there are two such terms which describe the same physical system. Some consequences of this result are discussed.

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