Inclusion Criteria:

   - Adult patients, >/= 18 years of age

   - Patients with documented relapsed or refractory AML, except acute promyelocytic
   leukemia (APL [M3 subtype]), or relapsed or refractory high-risk MDS (high-risk MDS
   defined as International Prognostic Scoring System (IPSS) Int-2 or high and >/= 10%
   blasts in bone marrow)

   - Eastern Cooperative Oncology Group (ECOG) performance status 0 to 2

   - Negative serum pregnancy test for women of childbearing potential and use of two forms
   of contraception while enrolled in the study and for 7 months after the patient
   discontinues from study

   - Male patients with female partners of childbearing potential must agree to use a latex
   condom and to advise their female partner to use an additional method of contraception
   during the study and for 2 months after the last dose of vismodegib

   - All non-hematological adverse events of any prior chemotherapy, surgery, or
   radiotherapy must have resolved to National Cancer Institute Common Terminology
   Criteria for Adverse Events (NCI CTCAE) Grade
   - Adequate hepatic and renal function

Exclusion Criteria:

   - Prior treatment with a Hh pathway inhibitor

   - Prior therapy for the treatment of malignancy within 14 days of Day 1, with the
   exception of:

Hydroxyurea in patients who need to continue this agent to maintain white blood cell (WBC)
counts
   - Current evidence of active central nervous system (CNS) leukemia

   - Any other active malignancy (except non-melanoma skin cancer or carcinoma in situ of
   the cervix)

   - Any severe and/or uncontrolled medical conditions or other conditions that could
   affect their participation in the study such as:

Unstable angina, symptomatic or otherwise uncontrolled arrhythmia requiring medication
(does not include stable, lone atrial fibrillation), or myocardial infarction before study treatment start Any active (acute or chronic) or uncontrolled
infection/disorders that impair the ability to evaluate the patient or for the patient to
complete the study

   - Pregnant or breast-feeding women

   - Patients who refuse to potentially receive blood products and/or have a severe
   hypersensitivity to blood products