Main Inclusion Criteria:  The patient has given written informed consent to participate in the study; Current diagnosis of RMS, based on the McDonald 2017 criteria ; Patients must have completed study GNC-401. Completion is defined as having performed the Week 48 assessments of study GNC 401; Have no clinical (relapses) or MRI signs (≥2 new T2 lesions of >10 mm diameter) of acute MS disease activity, based on the Week 48 MRI of study GNC 401, or, if yes, been retreated prior to study entry with rituximab; Have a B cell count ≤0.05 x 109 CD19 cells/L (assessed at the end of study GNC 401, or before inclusion in this study GNC 402 (available result from routine clinical practice); if not retreated with rituximab before entering study GNC-402, monthly B-cell count will be executed and retreatment will be considered by the treating physician when B-cells are >0.05 x 109 CD19 cells/L);  Main exclusion criteria  The emergence of any disease diagnosis during the course of study GNC-401 that is not due to MS and could better explain the patient's neurological signs and symptoms; Body weight ≤40 kg; Contraindication to continue rituximab therapy; Has received rituximab less than 12 days prior to study entry;  Use of any of the following medications since Week 48 of the GNC 401 study:  Interferon (IFN) β, glatiramer acetate, IV immunoglobulin (IVIG), dimethyl fumarate or teriflunomide; Natalizumab, mitoxantrone, cladribine, alemtuzumab, cyclophosphamide, systemic cytotoxic therapy, total lymphoid irradiation, and/or bone marrow transplantation; Highly potent immune modulating therapy, such as: ocrelizumab, ofatumumab, fingolimod, siponimod, ozanimod or anti-cytokine therapy, plasmapheresis or azathioprine; Any experimental drugs for the treatment of MS; Common Terminology Criteria for Adverse Events (CTCAE) Grade 2 or greater lymphopenia (based on Week 48 of study GNC 401);  Any major medical or psychiatric disorder that would affect the capacity of the patient to fulfill the requirements of the study, including:  Diagnosis or history of schizophrenia; Current diagnosis of moderate to severe bipolar disorder, major depressive disorder, major depressive episode, history of suicide attempt, or current suicidal ideation; Current or past (within the last 2 years) alcohol or drug abuse; History or presence of serious or acute heart disease such as uncontrolled cardiac dysrhythmia or arrhythmia, uncontrolled angina pectoris, cardiomyopathy, or uncontrolled congestive heart failure (New York Heart Association [NYHA] class 3 or 4); Known inability to undergo an MRI scan; Contraindications to the use of 5% glucose solution for infusion; Inability to follow study instructions, or complete study assessments, as defined by the protocol; Any history of cancer with the exceptions of basal cell carcinoma and/or carcinoma in situ of the cervix, and only if successfully treated by complete surgical resection, with documented clean margins and any medically unstable condition as determined by the Investigator; Pregnant or breastfeeding women; Abnormal liver function tests: aspartate aminotransferase (AST) or alanine aminotransferase (ALT) >2 times upper limit of normal range (ULN), or conjugated bilirubin >2 times ULN, or alkaline phosphatase (AP) or gamma-glutamyl transferase (GGT) >3 times ULN;