This trial aims to evaluate the effect of the transplantation of unmatched bone marrow derived mesenchymal stem cells in the treatment of acute graft versus host disease occurring as a result of a previous donated haematopoietic stem cell transplant. The study is being conducted at the Mater Medical Research Institute and Mater Health in Brisbane and is expected to enrol nine subjects. All participants will receive donated, unmatched, bone marrow derived mesenchymal stem cells and one of three different, escalating doses. Participants will be monitored for complications and assessed for changes in their clinical condition.