In the next-to-minimal supersymmetric model (NMSSM) a light CP-odd Higgs boson is so far allowed by current experiments, which, together with a large tan-beta, may greatly enhance the rare dileptonic decays. We examine these decays paying special attention to the new operator allowed by the light CP-odd Higgs boson. We find that in the parameter space allowed by current experiments like LEP II and b-> s gamma, the branching ratios of these rare decays can be greatly enhanced and thus the existing experimental data on B-> X_s mu^+ mu^- can further stringently constrain the parameter space (especially the region with a super-light CP-odd Higgs boson and large tan-beta). In the surviving parameter space we give the predictions for other dileptonic decay branching ratios and also show the results for the forward-backward asymmetry. After its publication, our work received much attention from international colleagues.

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