Twenty patients suffering from malignant hemopathies (mean age 31.7 years) were given hyperfractionated total body irradiation (TBI) (120 cGy/3 fractions per day: total dose = 1440 cGy/4 days) as conditioning for T-depleted HLA identical allogeneic bone marrow transplantation. At an average of 12 months (range of 4.5-22 months) follow-up there were two cases of early death and two cases (11%) of rejection. There were no cases of acute or chronic graft versus host disease (GVHD) nor cases of interstitial pneumonitis. The average time for durable engraftment was 22 days. Disease-free survival at 12 months was 65%. To improve the results and further reduce the percent of rejection, the authors propose intensifying the immunosuppressive conditioning by increasing the cyclophosphamide dose and that of TBI so that a total dose of 1560 cGy is reached.