Clinical Trial in Patients With Barth Syndrome- 4TAZPower

Key Inclusion Criteria: 1. Willing and able to provide signed informed consent form (ICF) prior to participation in any trial-related procedures. If applicable, informed consent in writing from parent(s) or legally-acceptable representative(s) and, informed assent from subject (if age appropriate according to local requirements) should be provided. 2. Agrees to adhere to the trial requirements for the length of the trial. 3. Must have genetically confirmed Barth Syndrome (pathogenic variant in the TAZ gene) 4. Male aged ≥ 5 years at time of the Screening Visit 5. Left Ventricular Ejection fraction of ≥ 50% by 3-D Echocardiogram at the Screening Visit. 6. For subjects with a medical history of cardiomyopathy, must be on a stable regimen (unchanged and constant) of background heart failure medications for at least 3 months prior to the Screening Visit. 7. Able to administer Investigational Medicinal Product (IMP) or have an appropriate designee who can administer the IMP (i.e., a capable family member or a caregiver). 8. Subjects with female partners of childbearing potential must be willing to use a highly effective method of contraception (e.g., abstinence, dual method of contraception) from the date they sign the ICF until 28 days after the last dose of IMP. Key Exclusion Criteria: 1. Unable to perform the required functional tests or undergo echocardiography. 2. History of solid organ transplant, except successful cardiac transplantation \> 12 months prior to screening, if, in the opinion of the Investigator, there is no evidence of organ rejection and post-transplant pharmacotherapy, is stable, and does not pose additional safety risk to participant. 3. Patients with an implantable cardioverter defibrillator (ICD) and with a known occurrence of ICD discharge in the 3 months prior to the Screening Visit. 4. Current placement on the waiting list for heart transplantation. 5. Hospitalization for heart failure within 6 months prior to the Screening Visit. 6. Any disease or medical condition that in the opinion of the Investigator would prevent the subject from successfully participating in the trial and reliably completing the assessments or might confound trial results. 7. Has a history of a systemic eosinophilic illness 8. Estimated Glomerular Filtration Rate (eGFR) of \< 30 mL/min at the Screening Visit (using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) 2021 formula for subjects \>16 years of age and the Schwartz 2009 formula for subjects 5-16 years of age). 9. Active malignancy or any other cancer from which the subject has been cancer-free for \< 2 years. Localized squamous or non-invasive basal cell skin carcinomas are allowed, if appropriately treated prior to Screening. 10. Participation in other investigational drug or device clinical trials within 30 days or 5 half-lives (whichever is longer) of Screening; or is currently enrolled in a non-interventional clinical trial that, in the opinion of the Investigator, may be potentially confounding to the results of the current trial. 11. History of allergic reaction to the IMP or any of its components. 12. Prior participation in any elamipretide trial or expanded access programs.