Spinal cord injury (SCI) leads to apoptosis of oligodendrocytes at the injury site resulting in demyelination and neuronal degeneration. This degeneration causes severe functional sensory and motor mutilations that remain an immense challenge to physicians and in which stem cell (SC) transplantation represents a viable alternative. This study is a phase I/II trial aimed at describing a method for treating patients with chronic complete spinal cord injuries (SCI) by utilizing autologous, purified CD34+ and CD133+ stem cells (SCs). The study focuses on the safety and efficacy of transplanting un-manipulated, autologous, purified stem cells in treated patients during a 5-year follow-up period.