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We report the results of a search for a charged Higgs boson in the decays of top quarks produced in pp̅ collisions at a center-of-mass energy of 1.96 TeV. We use a data sample corresponding to an integrated luminosity of 193 pb-1 collected by the upgraded Collider Detector at Fermilab. No evidence for charged Higgs production is found, allowing 95% C.L. upper limits to be placed on BR(t→ H+b) for different charged Higgs decay scenarios. In addition, we present in the minimal supersymmetric standard model (mH±, tan β) plane the first exclusion regions with radiative and Yukawa coupling corrections.