Inclusion Criteria:

- Biopsy-proven (no needle aspirations or cytologies) aggressive B-cell non-Hodgkin's
lymphoma (NHL), including 1 of the following histology subtypes:

- Diffuse large cell NHL

- Burkitt's or Burkitt-like NHL

- Primary mediastinal NHL

- Relapsed or refractory disease

- Bidimensionally measurable disease

- Transformed NHL allowed

- Not eligible for stem cell transplantation (for patients registered to study at first
relapse)

- No active CNS involvement by lymphoma

- Zubrod performance status 0-2

- No history of allergic reactions attributed to compounds of similar chemical or
biologic composition to PXD101

- Absolute neutrophil count >= 1,500/mm^3

- Platelet count>=100,000/mm^3

- WBC >= 3,000/mm^3

- Creatinine < 2 times upper limit of normal (ULN) OR creatinine clearance >= 60 mL/min

- No significant EKG abnormalities

- Bilirubin normal

- SGOT/SGPT < 2.5 times ULN (=< 5 times ULN if liver involvement)

- No long QT syndrome or marked baseline prolongation of QT/QTc interval (e.g.,
repeated demonstration of QTc interval > 500 msec)

- No other significant cardiovascular disease, including any of the following:

- Unstable angina pectoris

- Uncontrolled hypertension

- Congestive heart failure related to primary cardiac disease

- Any condition requiring anti-arrhythmic therapy

- Ischemic or severe valvular heart disease

- Myocardial infarction within the past 6 months

- No major surgery within 28 days prior to study entry

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No concurrent medication that may cause Torsades de Pointes (i.e., prolongation of
the QT interval > 500 msec)

- At least 14 days since prior radiotherapy

- At least 2 weeks since prior valproic acid or any other histone deacetylase inhibitor

- No clinical evidence of any of the following:

- Severe peripheral vascular disease

- Diabetic ulcers or venous stasis ulcers

- History of deep venous or arterial thrombosis within the past 3 months

- Radioimmunotherapy is considered a chemotherapy regimen

- Single-agent rituximab is not considered a chemotherapy regimen

- Standard salvage chemotherapy followed by autologous stem cell transplantation is
considered 1 regimen

- No known AIDS or HIV-associated complex

- Not pregnant or nursing

- Fertile patients must use effective contraception

- No other malignancy within the past 5 years except adequately treated basal cell or
squamous cell skin cancer or in situ carcinoma of the cervix

- At least 2 weeks since prior therapy and recovered

- No more than 5 prior chemotherapy regimens