For each subject the study will consist of two phases: a treatment phase and a follow-up phase. Screening procedures will take place within 28 days of baseline.

Treatment Phase: Subjects who qualify for enrollment into the study will receive single-agent CC-5013 in 28-day cycles. Study visits will occur every 4 weeks and hematologic and myeloma paraprotein laboratory assessments will occur every 2 weeks for the first 6 cycles and every 4 weeks thereafter.

Follow-Up Phase: All subjects who discontinue the treatment phase for any reason will continue to be followed for survival and post-treatment phase anti-myeloma treatment.

Inclusion Criteria:

• Understand and voluntarily sign an informed consent form.
• Age greater than or equal to 18 years at the time of signing the informed consent form.
• Must have a diagnosis of multiple myeloma and have relapsed and refractory disease. Such subjects have relapsed after having had at least a partial myeloma paraprotein response (greater or equal to 50% reduction of myeloma paraprotein) to prior therapy and then continued to develop disease progression despite salvage anti-myeloma therapy. Subjects must have documented evidence of disease progression during therapy with the last prior anti-myeloma treatment regimen (must have received at least 2 cycles) prior to study enrollment.Subjects may have been previously treated with thalidomide and/or radiation therapy.
• Measurable levels of myeloma paraprotein in serum (greater or equal to 0.5 g/dL) or urine (greater or equal to 0.2 g excreted in a 24-hour collection sample).
• Eastern Cooperative Oncology Group (ECOG) performance status score of 0, 1, or 2 (see Appendix II).
• Able to adhere to the study visit schedule and other protocol requirements
• Women of childbearing potential (WCBP) must have a negative serum or urine pregnancy test within 7 days of starting study drug.

Exclusion Criteria:

• Sexually active WCBP must agree to use adequate contraceptive methods (oral, injectable, or implantable hormonal contraceptive; tubal ligation; intra-uterine device; barrier contraceptive with spermicide; or vasectomized partner) while on study drug.
• WCBP must agree to have pregnancy tests every 4 weeks while on study drug (every 14 days for women with irregular cycles) and 4 weeks after the last dose of study drug.
• Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form.
• Pregnant or lactating females.
• Any of the following laboratory abnormalities:

A) Absolute neutrophil count (ANC) <1,000 cells/mm^3 (1.0 x 10^9/L) B) Platelet count <75,000/mm^3 (75 x 10^9/L) C) Serum creatinine >2.5 mg/dL (221 umol/L) D) Serum SGOT/AST or SGPT/ALT >3.0 x upper limit of normal (ULN) E) Serum total bilirubin >2.0 mg/dL (34 umol/L)

• Any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study.
• Prior history of malignancies other than multiple myeloma (except for basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix or breast) unless the subject has been free of the disease for greater than or equal to 3 years.
• Prior greater than or equal to grade 3 allergic reaction/hypersensitivity to thalidomide.
• Prior greater than or equal to grade 3 rash or any desquamating (blistering) rash while taking thalidomide.
• Prior use of CC-5013.
• Use of any standard/experimental anti-myeloma drug therapy within 28 days of the initiation of study drug therapy or use of any experimental non-drug therapy within 56 days of the initiation of study drug therapy