APPLICATION FOR PERMISSION TO FILE SUCCESSIVE HABEAS

Before DAVIS, JONES and DeMOSS, Circuit Judges. W. EUGENE DAVIS, Circuit Judge:

Richard William Kutzner was convicted and sentenced to death by a jury in Montgomery County Texas in September 1997 for the murder of Kathryn Harrison. He is currently scheduled to be executed, August 7, 2002. Kutzner’s conviction was affirmed by the Texas Court of Criminal Appeals, Kutzner v. State, 994 S.W.2d 180 (Tex.Crim.App.1999). He did not seek a writ of certiorari from the United States Supreme Court.

Kutzner sought habeas relief in the Texas state court and relief was denied by the Texas Court of Criminal Appeals. He then sought federal habeas relief which was denied in the district court and this court denied Kutzner a certificate of ap-pealability. Kutzner v. Johnson, 242 F.3d 605 (5th Cir.2001).

On August 5, 2002, Kutzner filed a petition in federal district court styled “Motion for DNA Testing” to form the basis for a motion for authorization to file a successive habeas petition. Kutzner sought a stay from the district court and argued that if he were permitted a stay and were permitted to conduct DNA testing, he would seek to file four claims in a successive federal habeas petition. The district court held that Kutzner had failed to demonstrate that he had any colorable new constitutional claims to offer that would qualify as a ground for a successive habeas petition under 28 U.S.C. § 2244(b). The district court then denied the application for stay and the request for DNA testing.

II.

Kutzner filed a notice of appeal from that ruling and an application for a certificate of appealability. Under the Anti-Terrorism and Effective Death Penalty Act (AEDPA), a petitioner must obtain authorization from , the Court of Appeals before filing a successive habeas corpus application. § 2244(b). This court is precluded from authorizing a successive petition unless the mover shows that the claim sought to be asserted is based on either newly discovered evidence or a new rule of constitutional law made retroactive to cases on collateral review by the Supreme Court that was previously unavailable. § 2244(b)(2)(a) and (b).

Although Kutzner made no application to this court for authorization to file a successive habeas petition, because of the press of time, we treat Kutzner’s notice of appeal and application for certificate of appealability as a motion for authorization to file a successive habeas application. Our focus is on whether Kutzner has demonstrated that the factual predicate for his claim could not have been discovered through the exercise of due diligence; and whether such facts, if proven, would have established that, but for the constitutional error, no reasonable fact finder could have found petitioner guilty of murdering Ms. Harrison. 28 U.S.C. § 2244(b)(2)(B)(I) and (ii).

During the investigation of Ms. Harrison’s murder, the police recovered scrap *336 ings of skin from under her fingernails and two strands of hair on her body. The fingernail scrapings and one of the hairs were disclosed to Kutzner before trial. Before trial neither the state nor Kutzner undertook to test either the fingernail scrapings or the hair then known to exist. Kutzner’s counsel argued to the jury that the identification of the killer was the sole issue before them and criticized the state for failing to test the nail scrapings and hair and produce DNA evidence that could have revealed the killer’s identity. As the district court noted, “Kutzner knew of the scrapings, blot, and first hair at trial, on appeal, during his state habeas petition and during his federal habeas petition. He never requested its testing.”

Kutzner raised three constitutional claims that allegedly could not have been presented earlier due to prosecutorial misconduct: (1) the State withheld potentially exculpatory evidence — a hair as well as a red substance on cellophane collected at the crime scene; (2) the State knowingly put on false testimony that no DNA testing of fingernail scrapings collected at the crime scene was possible; and (3) the State allowed false testimony concerning the scrapings to go uncorrected. However, Kutzner fails to establish Brady 1 or Giglio 2 error that would qualify for successive habeas relief.

To establish a Brady v. Maryland claim, Kutzner must prove that the prosecution suppressed favorable, material evidence that was not discoverable through due diligence. 373 U.S. at 87, 83 S.Ct. 1194; Rector v. Johnson, 120 F.3d 551, 558 (5th Cir.1997). Brady does not obligate the State to furnish a defendant with exculpatory evidence that is fully available to the defendant through the exercise of reasonable diligence. Rector, 120 F.3d at 558. When evidence is equally available to both the defense and the prosecution, the defendant must bear the responsibility of failing to conduct a diligent investigation. Herrera v. Collins, 954 F.2d 1029, 1032 (5th Cir.1992), aff'd, 506 U.S. 390, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993). In this sense, Brady applies only to “the discovery, after trial[,] of information which had been known to the prosecution but unknown to the defense.” United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976).

In this case, essentially all of the “suppressed” evidence was discussed at trial when State’s witness Peggy Frankhouser was cross-examined by Kutzner regarding the biological evidence collected at the crime scene.

It is clear from the exchange with this witness that Kutzner understood that at least one hair, possibly “a couple,” were collected at the crime scene. To the extent that Kutzner argues that a second hair was suppressed, it appears that Ms. Frankhouser’s memory was somewhat incomplete; however, the issue was not pursued. Kutzner was also aware that fingernail scrapings were gathered but not tested. Further, the cellophane was discussed twice. No evidence was suppressed and trial counsel could have tested any piece of it at the time of trial. Kutzner fails to demonstrate that prosecu-torial misconduct in this regard prevented him from discovering the factual basis of his successive claims at the time his first habeas petition was litigated.

*337 Similarly, Kutzner fails to prove the elements of Giglio v. United States, ie., that the State knowingly presented or failed to correct materially false testimony during trial. 405 U.S. at 153-54, 92 S.Ct. 763; Kutzner v. Johnson, 242 F.3d at 609. Importantly, due process is not implicated by the prosecution’s introduction or allowance of false or perjured testimony unless the prosecution actually knows or believes the testimony to be false or perjured; it is not enough that the testimony is challenged by another witness or is inconsistent with prior statements. Kutzner, 242 F.3d at 609; Koch v. Puckett, 907 F.2d 524, 531 (5th Cir.1990); United States v. Sutherland, 656 F.2d 1181, 1203 (5th Cir.1981).

As Ms. Frankhouser’s testimony makes clear, she was unsure of the number of hairs collected and offered to consult her notes on the matter. Kutzner did not pursue the matter further. Moreover, Frankhouser testified that no DNA testing was conducted on the fingernail scrapings, not that no DNA testing was possible. Once again, Kutzner chose not to pursue the matter. As stated above, Kutzner even argued the dearth of scientific evidence to the jury as proof of reasonable doubt. See, e.g., 13 SR 107-09.

The evidence proving Kutzner’s guilt was certainly circumstantial, but it was not weak. Tie wraps and electrical wiring used to restrain the victim and choke her were linked to Kutzner. Further, multiple items — money orders, a VCR, and a computer keyboard — taken from the two crime scenes were traced back to Kutzner. Also and perhaps most damaging was evidence that Kutzner committed another murder in Harris County about two weeks earlier with striking similarities to the Harrison murder. In light of this evidence, DNA exclusions or identifications from fingernail scrapings or stray hairs could not have affected the outcome of this case. Both victims were murdered in a place of business where dozens — possibly hundreds — of people had unwittingly deposited genetic material over the preceding months. Petitioner focuses on the single strand of hair that the state discovered since the trial. But even if this hair is tested and it is determined not to belong to Kutzner, this would not be persuasive evidence of his innocence. This is particularly true in light of the state’s strong circumstantial evidence of guilt. As a result, Kutzner fails to make a prima facie showing that DNA tests would prove his innocence of the murder of Kathryn Harrison.

For the reasons stated above, Kutzner has failed to meet the successive petition requirements of the AEDPA because:

1) Petitioner does not rely on a new rule of constitutional law;

2) He has not demonstrated that the predicate facts for his claims could not have been discovered previously through the exercise of due diligence; and

3) Even if the tests of hair and nail scrapings revealed that they belonged to someone other than Kutz-ner, this would be insufficient to establish by clear and convincing evidence that, but for constitutional error, no reasonable factfinddr would have found the applicant guilty of the underlying offense.

III.

Kutzner argues that we should not treat his pleadings filed in the district court and in this court as an application to file a successive habeas petition. He relies on McFarland v. Scott, 512 U.S. 849, 114 S.Ct. 2568, 129 L.Ed.2d 666 (1994), and its holding that appointed counsel and a stay *338 of execution is available in a post conviction proceeding under § 2254 or § 2255. We do not agree with Kutzner, however, that this right to a stay of execution is absolute.

The core concern of McFarland — that an un-counseled prisoner would be required to “proceed without counsel in order to obtain counsel and thus would expose him to the substantial risk that his habeas claims never would be heard on the merits,” 512 U.S. at 856, 114 S.Ct. 2568 — is not implicated here. Kutzner was represented by qualified counsel appointed under section 848(q)(4)(B) and his original § 2254 petition was fully litigated on the merits. Further, current counsel has represented Kutzner for more than one year. “The McFarland Court was concerned only with that period of time between the habeas petitioner’s motion for the appointment of counsel and the filing of the initial petition.” Turner v. Johnson, 106 F.3d 1178, 1182 (5th Cir.1997) (emphasis added). Thus, McFarland does not justify appointment of counsel or stay of execution for the preparation of a second federal habeas petition.

Finally, a federal court is without jurisdiction to consider a request for stay of execution in connection with a successive habeas petition “in the absence of express authorization by this [Cjourt pursuant to 28 U.S.C. § 2244(b)(3)(A).” Martinez v. Texas Court of Criminal Appeals, 292 F.3d 417, 423 (5th Cir.), cert. denied, - U.S. -, 122 S.Ct. 1992, 152 L.Ed.2d 1046 (2002). For reasons stated above, such authorization is not warranted in this case. Kutzner had sufficient time to seek appointment of counsel, investigate the instant claims, and litigate them in his original habeas petition because the bases of Kuztner’s claims were available to him since the time of trial proceedings. Allowance of a stay of execution under these circumstances would signal tacit approval of endless stays for the preparation of endless successive petitions.

Kutzner also argues that his motion for assistance to prepare a successive petition should — like a Rule 60(b) motion— not be characterized as an attempt to file a successive petition. Contrary to Kutzner’s argument, a motion under Rule 60(b) is the equivalent of a second or successive habeas petition subject to the standards of section 2244(b). Hess v. Cockrell, 281 F.3d 212, 214-15 (5th Cir.2002); Fierro v. Johnson, 197 F.3d 147, 151 (5th Cir.1999), cert. denied, 530 U.S. 1206, 120 S.Ct. 2204, 147 L.Ed.2d 237 (2000); United States v. Rich, 141 F.3d 550, 551-52 (5th Cir.1998). Like a Rule 60(b) motion, Kuztner’s motions for DNA testing and stay of execution in the lower court essentially attacked his conviction and sentence on constitutional grounds by leveling accusations of prosecutorial misconduct. Although his protestations are without merit, Kutzner has no other explanation for why he did not raise the instant issues earlier. Thus, there is no functional distinction between Kutzner’s motions and a request for successive habeas relief.

Nevertheless, even assuming arguendo that Kutzner’s appeal should be considered an application for certificate of appealability (“COA”), he is not entitled to relief. It is well settled that the Court’s appellate jurisdiction in habeas cases is premised on 28 U.S.C. § 2253(c)(1)(A). The COA standard to be applied is whether Kuztner “has made a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2); Barefoot v. Estelle, 463 U.S. 880, 893, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983); Dowthitt v. Johnson, 230 F.3d 733, 740 (5th Cir.2000), cert. denied, 532 U.S. 915, 121 S.Ct. 1250, 149 L.Ed.2d 156 (2001). This standard “includes showing that reasonable jurists could debate wheth *339 er (or, for that matter, agree that) the petition should have been resolved in a different manner or that the issues presented were adequate to deserve encouragement to proceed further.” Slack v. McDaniel, 529 U.S. at 483-84, 120 S.Ct. 1595, 146 L.Ed.2d 542 (internal quotations and citations omitted); Dowthitt, 230 F.3d at 740.

Ordinarily, “the determination of whether a COA should issue must be made by viewing the petitioner’s arguments through the lens of the deferential scheme laid out in 28 U.S.C. § 2254(d).” Barrientes v. Johnson, 221 F.3d 741, 772 (5th Cir.2000), cert. dismissed, 531 U.S. 1134, 121 S.Ct. 902, 148 L.Ed.2d 948 (2001). However, because Kuztner’s appeal is functionally a second or successive petition for habeas relief, Fierro v. Johnson, 197 F.3d at 151, Kutzner’s claims should be viewed “through the lens” of 28 U.S.C. § 2244(b)(2). In essence, the issue is whether it is debatable that Kutzner has substantially proved the elements of section 2244(b)(2)(B)(i) & (ii) — constitutional error and actual innocence established by newly discovered evidence. Therefore, under either standard this appeal is merit-less.

CONCLUSION.

For reasons stated above, we treat Kutzner’s filings as a petition for authority to file a successive habeas. We conclude that Kutzner has failed to meet the successive petition requirements of 28 U.S.C. § 2244(b)(2)(B)© and (ii). We, therefore, deny petitioner authority to file a successive habeas petition. We also deny his motion for stay of execution.

Notes

. Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963).

. Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).