We perform a search for a charged Higgs Boson (H +) lighter than the top quark, in the decay of top quark pairs. The search assumes no couplings to H+ except the Standard Model (SM) couplings. The modified Higgs sector of the SM we consider is one with two complex scalar doublet fields, with the so-called Model II couplings. We assume in this search that BR(t → W+b) + BR( t → H+b) = 1. Our search covers the parameter space 0.3 < tan beta < 150 , and 50 mH+ < 160 GeV. At 95% confidence, we exclude the existence of H+ at mH+ = 50 GeV for tan beta > 29 GeV. No limit can be set for mH+ > 140 GeV.