Inclusion Criteria:

   - Signed informed consent form (ICF)

   - Age 18 to 55 years (inclusive) as of the date the ICF was signed

   - Diagnosis of MS per update of McDonald criteria

   - Onset of MS symptoms (as determined by a neurologist; could be retrospectively) within
   10 years of the date the ICF was signed

   - Expanded Disability Status Scale (EDSS) score 0.0 to 5.0 (inclusive) at Screening

   - Greater than or equal to (>=) 2 MS attacks (first episode or relapse) occurring in the
   24 months prior to the date the ICF was signed, with >=1 attack in the 12 months prior
   to the date the ICF was signed, with objective neurological signs confirmed by a
   physician, nurse practitioner, or other Genzyme-approved health-care provider and the
   objective signs could be identified retrospectively

   - >=1 MS relapse during treatment with a beta interferon therapy or glatiramer acetate
   after having been on that therapy for >=6 months within 10 years of the date the ICF
   was signed

   - MRI scan demonstrating white matter lesions attributable to MS and meeting at least 1
   of the following criteria, as determined by the neurologist or a radiologist: >=9 time
   constant 2 (T2) lesions at least 3 millimeter (mm) in any axis; a gadolinium- (Gd-)
   enhancing lesion at least 3 mm in any axis plus >=1 brain T2 lesions; and a spinal
   cord lesion consistent with MS plus >=1 brain T2 lesion

Exclusion Criteria:

   - Received prior therapy with alemtuzumab

   - Current participation in another clinical study or previous participation in CAMMS323
   (Comparison of Alemtuzumab and Rebif Efficacy in Multiple Sclerosis, CARE-MS I)

   - Treatment with natalizumab, methotrexate, azathioprine, or cyclosporine in the past 6
   months. Participants who received one of these medications more than 6 months before
   the date the ICF was signed were eligible for study entry if approval was granted by
   Genzyme

   - Any progressive form of MS

   - History of malignancy (except basal skin cell carcinoma)

   - CD4 +, CD8 +, CD19 + (that is, absolute CD3 + CD4 + , CD3 + CD8 + , or CD19 + /mm 3 )
   count, absolute neutrophil count less than (<) lower limit of normal (LLN) at
   screening; if abnormal cell count(s) returned to within normal limits (WNL),
   eligibility could be reassessed

   - Known bleeding disorder (for example, dysfibrinogenemia, factor IX deficiency,
   hemophilia, Von Willebrand's disease, disseminated intravascular coagulation,
   fibrinogen deficiency, or clotting factor deficiency)

   - Significant autoimmune disease including but not limited to immune cytopenias,
   rheumatoid arthritis, systemic lupus erythematosus, other connective tissue disorders,
   vasculitis, inflammatory bowel disease, severe psoriasis

   - Presence of anti-thyroid stimulating hormone (TSH) receptor (TSHR) antibodies (that
   is, above the LLN)

   - Active infection or at high risk for infection