On January 22, 1997, Petitioner Randy Greenawalt filed a notice of appeal from the district court’s order denying his petition for a writ of habeas corpus filed pursuant to 28 U.S.C. § 2241 and filed a motion for a stay of execution. It is clear that Greenawalt is attempting to avoid the limitations imposed on successive petitions by styling his petition as one pursuant to § 2241. The Supreme Court has instructed us that the authority of the federal courts to grant habeas relief to state prisoners under § 2241 is limited by 28 U.S.C. § 2254 . Felker v. Turpin, — U.S. -, - - -, 116 S.Ct. 2333 , 2339 — 40, 135 L.Ed.2d 827 (1996). We, therefore, treat Greenawalt’s notice of appeal as an application for an order authorizing the district court to consider his successive petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2244 (b)(3)(A).

On April 24, 1996, the President signed into law the Antiterrorism and Effective Death Penalty Act of 1996, Pub.L. No. 104-132,110 Stat. 1214,1217-26 (1996) (“the 1996 Act”), which placed new limitations on the presentation of a successive claim. Under the 1996 Act, section 2244(b)(2) now requires the dismissal of a successive petition unless:

28 U.S.C. § 2244 (b)(1) & (2).

Greenawalt alleges in his successive petition that the execution of a person convicted of murder in the first degree by lethal injection violates his federal constitutional rights.

On January 21,1997, the Arizona Supreme Court denied Greenawalt’s petition for review and for special action. Greenawalt now seeks review by the district court of his successive petition. Greenawalt has failed to demonstrate to this court, however, that he is relying on a new rule of constitutional law that has been made retroactive to habeas corpus application by the Supreme Court. Furthermore, his claim that execution by lethal injection violates his federal constitutional rights is not relevant to the question whether he is guilty of murder in the first degree. Thus, Greenawalt has not made a prima facie showing that he has satisfied the requirements of section 2244(b)(2). Accordingly, we are compelled to dismiss Greena-walt’s application for an order authorizing the district court tó consider Greenawalt’s successive petition for a writ of habeas corpus. We decline to issue a stay of execution because Greenawalt has not demonstrated that he could state a claim that would survive the restrictions set forth in § 2244(b)(2)(A) & (B).

The applications for authorization to file a successive petition for habeas corpus and for a stay of the execution are DENIED.

. We would be obliged to dismiss an appeal from the district court’s order under 28 U.S.C. § 2253 (c)(1)(A), which requires a certificate of appealability.