Inclusion Criteria:

- Patients with relapsing multiple myeloma (MM)

- Patients must have adequate platelet count of > 20,000 x 10^9/L, independent of
transfusions, unless it is due to massive myeloma infiltration.

- Anticipated life expectancy of at least 3 months

- Ejection fraction by echocardiogram (ECHO) or multiple gated acquisition (MUGA) scan
performed within 60 days prior to registration; left ventricular ejection fraction
(LVEF) > 40% by ECHO or MUGA.

- Female patients of child bearing age are required to have a negative pregnancy test
as indicated in thalidomide safety guidelines

- Patients must have a performance status of 0-2 based on Southwest Oncology Group
(SWOG) criteria. Patients with a poor performance status (3-4), based solely on bone
pain, will be eligible.

- All patients must be informed of the investigational nature of this study and must
have signed an institutional review board (IRB)-approved informed consent in
accordance with institutional and federal guidelines.

Exclusion Criteria:

- Evidence of central nervous system (CNS) involvement

- Grade > 2 peripheral neuropathy

- Hypersensitivity to Velcade, boron, or mannitol

- Recent (< 6 months) myocardial infarction, cerebrovascular accident (CVA)/stroke,
unstable angina, difficult to control congestive heart failure, uncontrolled
hypertension, or difficult to control cardiac arrhythmias.

- Evidence of chronic obstructive or chronic restrictive pulmonary disease.

- Prior malignancy, except for adequately treated basal cell or squamous cell skin
cancer, in situ cervical cancer, or other cancer for which the patient has been
disease free for at least three years.

- Patients must not have significant co-morbid medical conditions or uncontrolled life
threatening infection.

- Pregnant or nursing women. Women of child-bearing potential must have a negative
pregnancy test documented within one week of registration. Women and men of
reproductive potential may not participate unless they have agreed to use an
effective contraceptive method for the duration of the study treatment.