 This phase I trial is studying the safety and potential efficacy of infusing non-human leukocyte antigen HLA matched ex vivo expanded cord blood progenitors following treatment with clofarabine and cytarabine for patients with acute myeloid leukemia AML. The combination of clofarabine, cytarabine Ara-C and granulocyte colony-stimulating factor G-CSF has been tested in earlier studies for the treatment of acute myeloid leukemia. In these previous clinical trials, this combination of drugs has been shown to have an anti-leukemia effect. However, the combination of clofarabine and Ara-C is profoundly myelosuppressive and immunosuppressive causing periods of neutropenia potentially lasting more than three weeks. During this period, patients are at increased risk of infections that can result in an increased risk of death. G-CSF is a growth factor that is used to help the white blood cells recover more quickly, but even with G-CSF, the use of clofarabine and Ara-C is often limited by the need to take long breaks between treatments to allow blood counts to recover. In our lab we have developed a method of growing or expanding blood stem cells cells that give rise to the blood system from umbilical cord blood. We are doing this study to find out if giving these expanded cells after chemotherapy is safe, helps the blood system recover more quickly from chemotherapy to allow shorter breaks between treatments, and decreases the risk of infection 