Inclusion Criteria:

        - Patients must be ≥ 1 and ≤25 years of age.

        Diagnosis: Patients with relapse or refractory AML must have measurable disease ( >M1
        marrow)

          -  1st or greater relapse, OR

          -  Failed to go into remission after 1st or greater relapse, OR

          -  Failed to go into remission from original diagnosis after 2 or more induction attempts

        Eligibility for patients with an M1 marrow; defined as >0.1% by flow or molecular testing
        (e.g. PCR).

          -  must include two serial marrows (at least 1-week apart) demonstrating stable or rising
             minimal residual disease (MRD) (i.e. not declining).

          -  Patients may have CNS or other sites of extramedullary disease. No cranial irradiation
             is allowed during the protocol therapy.

          -  Patients with secondary AML are eligible.

          -  Patients with Down syndrome are eligible.

          -  Patients with DNA fragility syndromes (such as Fanconi anemia, Bloom syndrome) are
             excluded.

        Performance Level:

        - Karnofsky >50% for patients >16 years of age and Lansky > 50% for patients ≤ 16 years of
        age (See Appendix II for Performance Scales)

        Prior therapy - Patients must have fully recovered from the acute toxic effects of all
        prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study.

          1. Cytoreduction with hydroxyurea: hydroxyurea can be initiated and continued for up to
             24 hours prior to the start of decitabine/vorinostat. It is recommended to use
             hydroxyurea in patients with significant leukocytosis (WBC >50,000/L) to control blast
             count before initiation of systemic protocol therapy.

          2. Patients who relapsed while they are receiving cytotoxic therapy: at least 14 days
             must have elapsed since the completion of the cytotoxic therapy, except Intrathecal
             chemotherapy.

        Hematopoietic stem cell transplant (HSCT):

        - Patients who have experienced their relapse after a HSCT are eligible, provided they have
        no evidence of acute or chronic Graft-versus-Host Disease (GVHD) and are off all transplant
        immune suppression therapy for at least 7-days (e.g. steroids, cyclosporine, tacrolimus).
        Steroid therapy for non-GVHD and/or non-leukemia therapy is acceptable.

        Hematopoietic growth factors:

        - It must have been at least 7 days since the completion of therapy with GCSF or other
        growth factors at the time of enrollment. It must have been at least 14 days since the
        completion of therapy with pegfilgrastim (Neulasta ®)

        Biologic (anti-neoplastic agent):

        -At least 7 days after the last dose of a biologic agent. For agents that have known
        adverse events occurring beyond 7 days after administration, this period must be extended
        beyond the time during which adverse events are known to occur. The duration of this
        interval must be discussed with the study chair.

        Monoclonal antibodies: At least 3 half-lives of the antibody must have elapsed after the
        last dose of monoclonal antibody (i.e. Gemtuzumab = 36 days)

        Immunotherapy: At least 42 days after the completion of any time of immunotherapy, e.g.
        tumor vaccines or CAR T-cell therapy.

        XRT: Cranio or craniospinal XRT is prohibited during protocol therapy. No washout period is
        necessary for radiation given to non-CNS chloromas; >90 days must have elapsed if prior
        TBI, cranio or craniospinal XRT.

        Prior Demethylating and/or HDAC Inhibitor Therapy: Patients who have received prior DNMTi
        (e.g. decitabine) and/or HDACi (e.g. vorinostat) therapy are eligible to participate in
        this Phase 1 study. At least 7 days must have passed from prior DNMTi or HDACi as a washout
        period.

        Renal and hepatic function: Patients must have adequate renal and hepatic functions as
        indicated by the following laboratory values:

        A. Adequate renal function defined as: Patient must have a calculated creatinine clearance
        or radioisotope GFR ≥ 70ml/min/1.73m2 OR a normal serum creatinine based on age/gender.

        B. Adequate Liver Function Defined as: Direct bilirubin < 1.5 x upper limit of normal (ULN)
        for age or normal, AND alanine transaminase (ALT) < 5 x ULN for age. The hepatic
        requirements are waived for patients with known or suspected liver involvement by leukemia.
        This must be reviewed by and approved by the study chair or vice chair.

        Adequate Cardiac Function Defined as: Shortening fraction of ≥ 27% by echocardiogram, OR
        ejection fraction of ≥ 50% by radionuclide angiogram (MUGA).

        Reproductive Function A. Female patients of childbearing potential must have a negative
        urine or serum pregnancy test confirmed within 1 week prior to enrollment.

        B. Female patients with infants must agree not to breastfeed their infants while on this
        study.

        C. Male and female patients of child-bearing potential must agree to use an effective
        method of contraception approved by the investigator during the study and for a minimum of
        6 months after study treatment.

        Exclusion Criteria:

          -  No NG or G-Tube administration of Vorinostat is allowed. Capsule must be swallowed
             whole or given as oral suspension.

          -  They are currently receiving other investigational drugs.

          -  There is a plan to administer non-protocol chemotherapy, radiation therapy, or
             immunotherapy during the study period.

          -  They have significant concurrent disease, illness, psychiatric disorder or social
             issue that would compromise patient safety or compliance, interfere with consent,
             study participation, follow up, or interpretation of study results.

          -  They have a known allergy to any of the drugs used in the study.

          -  Patients with DNA fragility syndromes are excluded (e.g. Fanconi Anemia, Bloom
             Syndrome)

          -  They are receiving valproic acid (VPA) therapy.

          -  Patients with Acute Promyelocytic Leukemia (APL, APML) are excluded

          -  Patients with documented active and uncontrolled infection at the time of study entry
             are not eligible