Inclusion Criteria:

• Patients who have a diagnosis of acute myeloid leukemia that is relapsed or refractory to at least one prior standard treatment. If patients have acute promyelocytic leukemia, they must be refractory to all trans retinoic acid (ATRA) and arsenic trioxide.
• Are at least 18 years of age.
• Have given written informed consent approved by Lilly and the ethical review board (ERB)/institutional review board (IRB) governing the site.
• Must have adequate hepatic and renal function.
• Have discontinued all previous therapies for cancer, including chemotherapy, radiotherapy, immunotherapy, cancer-related hormonal therapy, or other investigational therapy for at least 30 days prior to study enrollment and recovered from the acute effects of therapy. Hydroxyurea used to control peripheral blood blast count is permitted within this 30-day period, but must be stopped at least 72 hours before study drug administration.
• Males and females with reproductive potential must agree to use medically approved contraceptive precautions during the trial and for 6 months following the last dose of study drug.
• Females of child bearing potential must have had a negative serum pregnancy test less than or equal to 7 days prior to the first dose of study drug.

Exclusion Criteria:

• Have received treatment within 30 days of the initial dose of study drug with a drug that has not received regulatory approval for any indication.
• Patients with chronic myeloid leukemia (CML)
• Have received an autologous or allogenic stem cell transplant within 90 days of the initial dose of study drug.
• Have previously completed or withdrawn from this study or any other study investigating LY573636 sodium.
• Have serious preexisting medical conditions that in the opinion of the investigator would preclude participation in this study.
• Have serious concomitant disorders, including active bacterial, fungal, or viral infection, incompatible with the study.
• Have a known coagulopathy or bleeding disorder, other than leukemic related thrombocytopenia. Patients with severe or life-threatening bleeding refractory to platelet transfusions are also excluded from this study.
• Major surgery within 4 weeks of study enrollment.
• Are receiving warfarin (Coumadin).
• Females who are pregnant or breast feeding.
• Have known positive results of HIV, hepatitis B or C.