Acute Myeloid Leukemia AML is a cancer in which the process of normal cell hematopoietic differentiation is disrupted. Evidence exists that AML comprises a hierarchy with leukemic stem cells giving rise to more differentiated, but immature and functionally incompetent populations. The similarity of these AML subpopulations to normal stages of hematopoietic differentiation has not been dissected comprehensively at the transcriptional level. Here we introduce Normal Memory Analysis (NorMA), a data analysis method that extracts from omic data the remnants of the healthy normal-like phenotype. Applying NorMA to gene expression data from AML uncovered a wealth of information in the normal-like component of data: the normal hematopoietic memory of AML tumor cells. We found significant variation within the patient population, and we found strong association of this normal hematopoietic memory with survival. We found that undifferentiated NorMA phenotype has significantly worse survival than differentiated NorMA phenotype, showing that the NorMA classification of tumors captures a biologically meaningful stratification of patients, with highly significant survival association. Patients with NorMA phenotype in the undifferentiated Hematopoietic Stem Cell HSC stage had the worst survival, with median survival time under 6 months. We further found significant survival differences between tumor groups with differentiated NorMA phenotype, depending on their hematopoietic path: AML patients with NorMA phenotype in megakaryocyte-erythroid progenitor MEP stage had significantly better survival than those with NorMA phenotype in granulocyte-macrophage progenitor GMP stage. Thus NorMA produced a stratification of AML cohorts by differentiation stage, with significant outcome differences. It also provided clean molecular signatures for these stages. NorMA can be used in many other contexts, to explore for example the tumor cell of origin, or disease predisposition.