Methods of selecting umbilical cord blood units for ex-vivo expansion, separation of CD133+/CD34+ positive and uncultured CD133+/CD34+ negative fractions, methods for expanding the selected CD133+/CD34+ fraction, selection of expanded populations of CD133+/CD34+ cord blood cells for transplantation to subjects in need thereof and the therapeutic use of suitable selected, ex-vivo expanded CD 133+/CD34+ and unselected CD133/CD34 negative cord blood fractions for transplantation in the clinical setting, for treatment of hematological malignancies are provided. The present invention also envisions kits comprising the expanded and unselected cord blood fractions.
