 This is a phase IIIa, randomized, double-blind, single-dose, placebo controlled, two-way crossover clinical trial in which 10 patients from 18 to 65 years of age affected with chronic traumatic spinal cord will enter the study with the objective to assess the safety and to obtain efficacy data in intrathecal administration L3 level of expanded Whartons jelly mesenchymal stem cells. Following the administration patients will remain for 24 h at the hospital and thereafter will be discharged. For the first period, the follow-up is planned at day 7 and at 1, 3 and 6 months. At month 6, the patients will be treated in a crossover way second period and will follow the same schedule for the follow-up. Results will be initially assessed at 12 month follow-up and thereafter at 24 and 36 months as part of a long-term follow-up. 