This trial aims to evaluate the safety and effectiveness of using cord blood to treat babies that have suffered a stroke. The trial is being conducted by the Children's Memorial Hermann Hospital and the University of Texas Health Science Centre, in conjunction with Cord Blood Registry Inc. Once diagnosed with having had a stroke around the time of birth (perinatal arterial ischaemic), the baby will be enrolled into the trial for transfusion with its own umbilical cord blood, provided this is available. The children will be monitored for complications and the clinical progress of each participant will be monitored for the next two years. The trial proposes to recruit 10 subjects between September 2012 and December 2015.