 The purpose of this research is to study a treatment program for patients with aggressive lymphoma that has come back after initial or first therapy called relapsed or that has not responded to first therapy called refractory. Since 1993, we have used a combination of chemotherapy known as ICE Ifosfamide, Carboplatin, and Etoposide for your type of lymphoma. In many patients, this treatment helps the disease to shrink before giving high-dose therapy and autologous stem cell transplant ASCT. Only patients who respond to these types of treatments have a chance of their disease going away remission with an ASCT. In 1999, we studied the same treatment but added another medicine for your type of lymphoma, Rituximab Rituxan, to the ICE treatment RICE. More patients had lymphoma shrinkage from this treatment chemosensitive disease than with ICE alone. These patients then received high dose therapy and autologous stem cell transplant and have an improved chance of having a remission. 