  In this work, we explore the flavour changing decays $H_i \to b s$ in a
general supersymmetric scenario. In these models, the flavour changing decays
arise at loop-level but, originating from a dimension-four operator, do not
decouple and may provide a first sign of new physics for heavy masses beyond
collider reach. In the framework of the minimal supersymmetric extension of the
Standard Model (MSSM), we find that the largest branching ratio of the lightest
Higgs ($H_1$) is ${\cal O}(10^{-6})$ after imposing present experimental
constraints. While heavy Higgs states may still present branching ratios ${\cal
O}(10^{-3})$. In a more general supersymmetric scenario, where additional Higgs
states may modify the Higgs mixings, the branching ratio BR($H_1 \to b s$) can
reach values ${\cal O}(10^{-4})$ , while heavy Higgses still remain at ${\cal
O}(10^{-3})$. Although these values are clearly out of reach for the LHC, a
full study in a linear collider environment could be worth pursuing.
