We discuss the constraints on the supersymmetric parameter space from the decay mode /b-->sγ for large values of /tanβ. We improve the theoretical prediction for the decay rate by summing very large radiative corrections to all orders in perturbation theory. This extends the validity of the perturbative calculation to the large /tanβ regime. This resummation of terms of order αsn tann+1β is based on a recently proposed effective Lagrangian for the Yukawa interaction of bottom quarks. Moreover, we identify an additional source of /tanβ-enhanced terms, which are of order αs tanβ and involve the charged Higgs boson, and analyse their behaviour in higher orders of perturbation theory. After correcting the current expressions for this rare decay branching ratio at next-to-leading order, we obtain that, contrary to recent claims, the measured branching ratio of /b-->sγ constrains the supersymmetric parameter space in a relevant way, even if /tanβ is large.