The goal of treatment of relapsed or refractory acute myeloid leukemia (AML) is to achieve remission and proceed to hematopoietic stem cell transplant (HSCT). Unfortunately, standard protocols have limited success. In this study the investigators will identify patients with relapsed or refractory AML who are unlikely to benefit from standard chemotherapy protocols and do not qualify for, or do not wish to participate in, institutional chemotherapy trials. Peripheral blood from a related haploidentical donor will be collected for the isolation of natural killer (NK) cells. NK cells will be induced into a memory-like state using cytokine supplementation only. In this Phase I/II study, patients will receive a lymphodepleting chemotherapy regimen, after which the cytokine-induced memory-like NK cells (CIML-NKs) will be infused. The primary study endpoint is the feasibility and safety of infusion of the cells. The secondary endpoints are efficacy, as measured by clinical response per standard criteria and ability to subsequently undergo allogeneic HSCT, and the persistence of memory-like NK cells in the blood.