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We consider three-point couplings in simple Lie algebras -- singlets intriple tensor products of their integrable highest weight representations. Acoupling can be expressed as a linear combination of products of finitely manyelementary couplings. This carries over to affine fusion, the fusion ofWess-Zumino-Witten conformal field theories, where the expressions are in termsof elementary fusions. In the case of su(4) it has been observed that there isa purely affine elementary fusion, i.e., an elementary fusion that is not anelementary coupling. In this note we show by construction that there is atleast one purely affine elementary fusion associated to every su(N>3).Comment: 9 pages, LaTe

PURELY AFFINE ELEMENTARY su(N) FUSIONS