Inclusion Criteria:

          -  Newly diagnosed mature B-lineage (CD20 positive) Leukemia/Lymphoma

          -  1. Diffuse Large Cell Lymphoma (NOT primary mediastinal B-cell lymphoma) -2. Burkitt's
             Lymphoma

          -  3. High Grade B-cell Lymphoma---Burkitt's like.

        B-Cell Anaplastic Large cell Ki 1 positive lymphomas, Primary Mediastinal B-Cell Lymphoma
        (PMBL), and B-Lymphoblastic lymphomas are ineligible.

        No previous chemotherapy. Patients who have received emergency irradiation and/or steroid
        therapy will be eligible ONLY if started on protocol therapy not more than 72 hours from
        the start of radiotherapy or steroids. Bone marrow and cerebrospinal fluid MUST be obtained
        before steroids are given for patient to be eligible for the study.

        Exclusion Criteria:

          -  Patients with newly diagnosed Group A (low risk) lymphoma. Patients with Group B
             (intermediate risk) if classified as Murphy Stage III/IV and diagnostic LDH > 2 XULN
             and patients with primary mediastinal B-cell lymphoma (PMBL).

          -  Patients who have received any steroids in the week prior to diagnosis except as
             stated in Section 4.1.4 of the protocol.

          -  No congenital or acquired immune deficiency. These patients are excluded due to the
             expected intense immunosuppression, increased risk of opportunistic infections, and
             higher expected septic death rate in this subgroup of patients with this proposed
             therapy.

          -  No prior solid organ transplantation.

          -  Patients with previous malignancies that have been treated with systemic chemotherapy
             with alkylator or anthracycline therapy. The latter group of patients are excluded due
             to an expected increase in late effects (eg. late cardiac toxicity, secondary
             malignancies, sterility, etc.).

          -  Patients with known G6PD deficiency are NOT ELIGIBLE for Rasburicase therapy. Patients
             with G6PD deficiency should be treated with alkalinization, IV hydration and po and/or
             IV allopurinol during the reduction phase (COP).

        4.2.6 Patients with serious (sepsis, pneumonia, etc..) proven or suspected infections at
        diagnosis will be excluded.

        4.2.7 Pregnancy or Breast-Feeding: No information is available regarding human fetal or
        teratogenic toxicities. Pregnancy tests must be obtained in girls who are post-menarchal.
        Males or females of reproductive potential may not participate unless they have agreed to
        use an effective contraceptive method.