This trial aims to evaluate the use of stem cells from the patient's own bone marrow in treatment of Multiple Sclerosis. The trial is being sponsored by Fundación Pública Andaluza Progreso y Salud and is being conducted at three University hospitals in Spain. They propose to recruit 30 patients between May 2012 and November 2014. All participants will have bone marrow stem cells harvested prior to commencement of the trial. Being a crossover study the subjects will be divided into two groups. The first group will receive the stem cell injection on the first day, while the second group will receive a placebo infusion. After 180 days, the second group will receive the stem cell injection and the first group a placebo injection. All participants will be monitored for complications following the transfusion and changes in clinical condition for one year.