To participate in this study, the patients also need to have a central line (a thin plastic catheter or tube that is placed during surgery into one of the large veins in the neck or chest). Central lines are used to give intravenous medications (go directly into the vein) or to take blood samples without the patient having to endure frequent needle sticks. Before the treatment starts, we will remove a small amount of the bone marrow (back-up bone marrow) and store it. The reason for this is that if the donors bone marrow or blood stem cells do not grow properly after the transplant and the patients blood counts stay low, we can put the patients own bone marrow cells back into their body. This will help the blood counts to recover, but this means that the patient will also have thalassemia again.