This paper calculates the amount of baryon/radiation isocurvature fluctuation produced through the decay of a curvaton field. It is shown, in particular, that if curvaton decay preserves the baryon number and the curvaton dominates the energy density at the time of decay, the initial curvaton/radiation isocurvature mode is entirely transferred into a baryon/radiation isocurvature mode. This situation is opposite to that previously studied in three fluid models of curvaton decay; this difference is related to the conservation of the preexisting baryon asymmetry and to the efficiency of the annihilation of all baryon/antibaryon pairs produced in the decay. We study in detail the relevant cases in which the curvaton decay preserves or not the baryon number and provide analytical and numerical calculations for each situation.