Corrected QT interval (QTc) > 475 millisecondsXx_NEWLINE_xXConcurrent medications associated with a known risk of corrected QT interval (QTc) prolongation and/or Torsades de Pointes are not allowed within 2 weeks of initiation of study treatment; those medications listed as a possible risk for causing QTc prolongation and Torsades de Pointes will be allowed, although if an alternative medication can be substituted, that would be preferable; granisetron is an acceptable antiemetic on this study, but if a patient must take ondansetron, they may NOT take any other concomitant agents which might impact their QTcXx_NEWLINE_xXPatients with current evidence of significant cardiovascular disease (New York Heart Association class III or IV cardiac disease), symptomatic congestive heart failure, dilated/hypertrophic or restrictive cardiomyopathy, myocardial infarction (within the past 6 months), unstable angina, unstable arrhythmia or a need for anti-arrhythmic therapy (use of medications for rate control for atrial fibrillation is allowed such as calcium channel blockers and beta-blockers, if stable medication for at least last month prior to initiation of romidepsin treatment and medication not listed as causing Torsades de Pointes), or evidence of acute ischemia on electrocardiogram (ECG); marked baseline prolongation of QT/QTc interval, e.g., repeated demonstration of a QTc interval > 450 msec*; long QT syndrome; the required use of concomitant medication that may cause Torsades de Pointes or may cause a significant prolongation of the QTc* Note: due to difficulties assessing QTc in patients with heart block, they may be eligible if deemed safe by a cardiologist; if a patient must take ondansetron as their antiemetic, their QTc may NOT be over 450 (no exception for patients with heart block)Xx_NEWLINE_xXPatients with significant cardiovascular disease (New York Heart Association class III or IV cardiac disease), symptomatic congestive heart failure, myocardial infarction within the past 6 months, unstable angina, unstable arrhythmia or a need for anti-arrhythmic therapy (use of frequency adjusting medication for atrial fibrillation is allowed, if stable medication for at least last month prior to initiation of belinostat treatment and medication not listed as causing Torsades de Pointes), or evidence of acute ischemia on electrocardiogram (ECG); marked baseline prolongation of QT/corrected QT (QTc) interval, e.g., repeated demonstration of a QTc interval > 450 msec; long QT syndrome; concomitant use of drugs known to prolong the QT interval and/or cause Torsades de Pointes is not allowed during the study or within 2 weeks of study entry; these drugs should also be avoided for up to 4 weeks following discontinuation of study treatment; drugs that may be associated with Torsades de Pointes but lack substantial evidence will be allowed at the discretion of the PI (although it is preferable to substitute an alternate medication), and patients will be closely monitoredXx_NEWLINE_xXHistory of familial long QT syndrome, or use of medications that may cause QTc interval prolongationXx_NEWLINE_xXPatients with baseline prolongation of the rate-corrected QT interval (QTc) (e.g., repeated demonstration of QTc interval > 480 milliseconds, or history of congenital long QT syndrome, or torsades de pointes) are ineligibleXx_NEWLINE_xXBaseline prolongation of the rate-corrected QT interval (QTc) (e.g. repeated demonstration of QTc interval > 480 milliseconds, or history of congenital long QT syndrome, or torsades de pointes)Xx_NEWLINE_xXPatients with baseline prolongation of the rate-corrected QT interval (QTc) (e.g., repeated demonstration of QTc interval > 480 milliseconds, or history of congenital long QT syndrome, or torsades de pointes)Xx_NEWLINE_xXBaseline prolongation of the rate-corrected QT interval (QTc) > 480 milliseconds, or history of congenital long QT syndrome, or torsades de pointesXx_NEWLINE_xXCorrected QT interval (QTc) of < 480 millisecondsXx_NEWLINE_xXBaseline prolongation of the rate-corrected QT interval (QTc) > 480 milliseconds or history of congenital long QT syndrome or Torsades de pointesXx_NEWLINE_xXBaseline electrocardiogram (EKG) shows normal corrected QT interval (QTc) interval of =< 470 milliseconds (ms)Xx_NEWLINE_xXKnown history of QT/corrected QT (QTc) prolongation or torsades de pointes (TdP); patients who are currently receiving treatment with medication with a known risk to prolong the QT interval or inducing torsades de pointes and the treatment cannot either be discontinued or switched to a different medication prior to starting study drugsXx_NEWLINE_xXCorrected QT (QTc) interval =< 480 millisecondsXx_NEWLINE_xXCorrected QT (QTc) interval =< 480 millisecondsXx_NEWLINE_xX