Cohort 1: Patients who are less than or equal to 65 years of age.

1. To determine the disease-free survival (DFS) in the 2 arms (standard dose versus high dose rituximab)

Cohort 2: Patients who are older than 65 years of age

1. To determine the disease-free survival (DFS) in the 2 arms (standard dose versus high dose rituximab)
2. To determine the treatment related mortality (TRM)

Carmustine, cytarabine, etoposide, melphalan, and rituximab are all standard chemotherapy drugs.

If you are found to be eligible to take part in this study, you will be randomly assigned (as in the toss of a coin) to one of two treatment groups. Participants in one group will receive high dose rituximab with transplantation and high dose chemotherapy. Participants in the other group will receive standard dose rituximab with transplantation and high dose chemotherapy. The first 10 patients enrolled on this study will have an equal chance of being assigned to either group. After the first 10 participants are enrolled, the remaining participants will have a higher chance of being assigned to the group that has proven to be more effective.

All participants will have a plastic tube (catheter) inserted under their collarbone. This catheter will be left in place for the entire treatment period. The catheter will be used to deliver most of the drugs and for the collection and transfusion of the stem cells. When possible, all drugs that need to be given by vein will be given using the catheter.

Stem cell collection is done on a separate study and patients will take part in this study only after the stem cell collection is complete. You should have an adequate number of stem cells collected and stored before you can be eligible for high-dose chemotherapy and transplantation.

All treatment will be given at M. D. Anderson. You will be admitted to the hospital to receive high dose chemotherapy and will stay in the hospital for 3-4 weeks. You will be given carmustine by vein over 1 hour on Day 1. On Days 2 - 5, you will be given cytarabine by vein over 1 hour and etoposide by vein over 3 hours. This will be repeated every 12 hours on Days 2-5. On Day 6, you will be given melphalan by vein over 30 minutes. On Day 7, the stem cells that were collected earlier will be given back to you ("transplanted") through the catheter over 30-45 minutes.

You will also receive either high dose or standard dose rituximab by vein over 4-6 hours one day after the transplant (Day 1) and then again 1 week later (Day 8).

You will receive G-CSF injections staring at Day 1 (one day after transplant or stem cell infusion). These will continue our cell count reaches the appropriate level for at least 3 days in a row. Blood tests (2 teaspoons) will be done every day while you are in the hospital to track the effects of the transplant.

You will be asked to return to M. D. Anderson at 3 months and 6 months after transplantation, then every 6 months for 3 years, and then once a year up to 5 years from the transplant date. At each visit you will get blood work (1-2 tablespoons), CT scans, and other tests like bone marrow (if needed) to determine the status of your lymphoma.

This is an investigational study. All of the drugs used in this study are FDA approved and are commercially available. Up to 100 patients will take part in this study. All will be enrolled at M. D. Anderson.

Inclusion Criteria:

1. Patients with histologically proven diffuse large B-cell (CD20 positive) or transformed follicular non-Hodgkin's lymphomas, that have relapsed after conventional chemotherapy and are not eligible for protocols of higher priority
2. Patients must have chemosensitive disease to salvage chemotherapy and less than 5% bone marrow involvement with lymphoma by gross pathologic examination
3. Age less than or equal to 80 years. There is no lower age limit for this study.
4. Zubrod performance status of less than 2
5. Negative pregnancy test in patients with child bearing potential
6. Must be willing to sign informed consent
7. Should be seronegative for HIV, hepatitis B surface antigen, hepatitis C antibody.

Exclusion Criteria:

1. Patients with known active CNS disease are excluded. Patients with prior history of CNS disease should have a negative MRI of the brain (and/or spine if indicated) and negative CSF cytology within 4 weeks of enrollment into the study.
2. Less than 3 weeks from last cytotoxic chemotherapy
3. Serum bilirubin > 1.5 mg/dl
4. Serum transaminases > 2X/ULN
5. Serum creatinine > 1.6 mg/dl
6. Failure to collect more than 3 x 1,000,000 CD34+ stem cells/kg body weight
7. Left ventricular ejection fraction of < 40%, unless cleared by cardiology
8. Corrected DLCO of < 50%
9. Patients who are on anticoagulants or antiplatelet agents.

4 Years, 5 Months