Effective Death Penalty Appeals Act This bill allows an individual sentenced to death by a state to present newly discovered evidence in a petition challenging the legality of the individual's detention (i.e., a habeas corpus petition). Under the bill, a federal court may grant a habeas corpus petition concerning such an individual if the death sentence was imposed without consideration of newly discovered evidence of the individual's probable innocence. Furthermore, a federal court may consider, subject to certain requirements, a subsequent petition concerning such an individual if the petition is based on a claim that the death sentence was imposed without consideration of newly discovered evidence of the individual's probable innocence. (Currently, if a federal court has already considered a habeas corpus petition concerning an individual, subsequent petitions concerning that individual shall be dismissed, with limited exceptions.)