
421 So.2d 1385 (1982)
Ronald JACKSON, Petitioner,
v.
Louie L. WAINWRIGHT, Secretary, Department of Corrections, State of Florida, Respondent.
No. 60271.
Supreme Court of Florida.
October 7, 1982.
Rehearing Denied December 13, 1982.
*1386 Bennett H. Brummer, Public Defender, and Karen M. Gottlieb and Elliot H. Scherker, Asst. Public Defenders, Eleventh Judicial Circuit, Miami, for petitioner.
Jim Smith, Atty. Gen., and Theda R. James, Asst. Atty. Gen., Miami, for respondent.
ADKINS, Justice.
By petition for writ of habeas corpus, petitioner (hereinafter referred to as defendant) asserts ineffective assistance by counsel on his direct appeal from his conviction and sentence of death, and, that because of this, he is entitled to a belated appellate review. The claim of ineffective assistance of counsel stems from acts or omissions before this Court in Jackson v. State, 366 So.2d 752 (Fla. 1978), cert. denied, 444 U.S. 885, 100 S.Ct. 177, 62 L.Ed.2d 115 (1979). We have jurisdiction. Art. V, *1387 § 3(b)(9), Fla. Const.; Fla.R.App.P. 9.030(a) (3); Knight v. State, 394 So.2d 997 (Fla. 1981).
Defendant has identified four legal errors which he contends his appellate counsel should have raised on direct appeal. He argues that the failure to present those issues denied him his rights to a full and meaningful appeal and to the effective assistance of appellate counsel as guaranteed by the sixth, eighth, and fourteenth amendments to the Constitution of the United States. These asserted legal errors include: 1) the trial court's admission of oral statements made by defendant during interrogation proceedings conducted after invocation of his Miranda rights; 2) the trial court's application of a nonstatutory aggravating circumstance, i.e., defendant's failure to display remorse for the offense; 3) the trial court's improper construction of mitigating circumstances, i.e., impaired mental state of defendant at the time of the offense and his inability to conform his conduct to the requirements of law; and, 4) the trial court's instructions to the jury that where one or more of the aggravating circumstances is found death is presumed to be the proper sentence, unless they are overridden by one or more of the mitigating factors. We have considered these assertions in light of the standards announced in Knight and find no substantial deficiency in defendant's representation on appeal by which he was prejudiced.
Defendant was first arrested by a Florida highway patrol officer and was immediately advised of his Miranda rights. Defendant invoked his right to remain silent, and interrogation ceased. Defendant was then turned over to Dade County officers and placed in the Dade County jail. Approximately four hours after defendant had invoked his privilege of remaining silent, Dade County officers gave defendant a fresh set of warnings. Defendant says his counsel should have challenged the admissibility of oral statements made by him during interrogations conducted after defendant's assertion of his fifth amendment right of silence. Instead, defendant says his counsel challenged the admissibility of the statements on other grounds, overlooking the merits of this claim which certainly had an "arguable chance of succeeding." We disagree.
In Jennings v. United States, 391 F.2d 512 (5th Cir.), cert. denied, 393 U.S. 868, 89 S.Ct. 154, 21 L.Ed.2d 136 (1968), it appeared that Jennings was first warned by Ft. Pierce, Florida, police of his Miranda rights. After Jennings answered a few questions he announced that he would not answer any further questions and the interrogation immediately stopped. Approximately one hour later, an agent of the Federal Bureau of Investigation arrived at the police station to interrogate Jennings. Proceeding as if there had been no prior interrogation, the FBI agent again gave full and complete warning. Subsequent to these warnings, the defendant signed a waiver and did not hesitate to discuss the matter with the agent. Jennings challenged the admissibility of the statements arguing that he had refused to answer any further questions from Fort Pierce police and it was improper, under Miranda, for the FBI agent to question him. The Court held that there was no error in the admission of the statement obtained by the FBI. It cannot be said that a challenge to the admissibility of the statement on this ground would have an "arguable chance of success," as to warrant the conclusion that defendant was prejudiced by his counsel's failure to review this argument on appeal, or that defendant's counsel provided ineffective assistance in failing to reargue this point.
Defendant argues that in the findings of fact supporting the sentence of death, the trial judge expressly relied upon, in addition to two statutory aggravating and two statutory mitigating factors, one nonstatutory aggravating factor, i.e., defendant's failure to display remorse for the offense.
The first paragraph of these findings of fact reads as follows:
That sufficient aggravating circumstances exist in this particular case that far outweigh any mitigating circumstances in the record. The death of this decedent *1388 occurred while the defendant was engaged in the commission of the crime of Armed Robbery. In addition thereto the defendant clearly committed the capital felony in order to eliminate the victim of the robbery. He forcibly transported the victim against her will, from the scene of the robbery to a lonely desolate area to accomplish the capital felony. These facts alone, in this Court's judgment could justify the imposition of the death penalty, but this particular killing is far more useless and heinous than this.

366 So.2d at 756 (emphasis added).
In the Court's reasoned judgment, these facts alone were sufficient to warrant the imposition of the death penalty, however, the Court also discussed the heinous nature of the crime, and then said:
The facts of this case are the most "heinous, atrocious and cruel" that this Court has ever considered. It is for crimes like the one at Bar that the death penalty is in fact appropriate. See Sullivan v. State, 303 So.2d 632 (Fla. 1974).
366 So.2d at 756.
In giving the reasons for the death sentence in this case, the trial judge was assuring himself that he was reaching a similar result to that reached under similar circumstances in another case. This reasoning process is exemplified by the cite to Sullivan. It was after this that the Court said:
This Court has observed the demeanor and the action of the defendant throughout this entire trial and has not observed any sign of remorse, indicating full well to this Court that the death penalty is the proper selection of the punishment to be imposed in this particular case.
366 So.2d at 756-57.
This was error. However, the defendant has the burden to show that this specific deficiency when considered under the circumstances of the individual case was substantial enough to demonstrate a prejudice to him to the extent that there is a likelihood that the deficient conduct affected the outcome of the proceedings. This means the deficiency must concern an issue which is error affecting the outcome, not simply harmless error. Knight v. State.
Although an improper aggravating circumstance (lack of remorse) was included in the findings of the trial judge's sentence decision and there were identified two mitigating circumstances (defendant's age and first conviction), nevertheless, Elledge v. State, 346 So.2d 998 (Fla. 1977), would not compel reversal of the sentence judgment in this case. It is apparent on the face of the findings by the trial judge that the result of the weighing process would not have been different had the impermissible factor not been present. Jackson, 366 So.2d at 756. It is beyond reason to conclude that the trial judge's decision to impose the death penalty would have been affected by the elimination of the unauthorized aggravating circumstance. Brown v. State, 381 So.2d 690 (Fla. 1980), cert. denied, 449 U.S. 1118, 101 S.Ct. 931, 66 L.Ed.2d 847 (1981). There was no substantial deficiency by appellate counsel and no prejudice stemming from the failure to raise this issue.
Defendant also says that appellate counsel should have questioned on appeal the trial court's failure to consider the impaired mental state of defendant at the time of the offense and his inability to conform his conduct to the requirements of law. It is apparent from the court's order that the trial judge did in fact consider these mitigating circumstances and further, that he weighed the evidence on this issue and resolved the factual conflicts in favor of the state. The record does not support defendant's contention, so the failure of appellate counsel to raise this issue is not an omission that was a serious deficiency. There was no prejudice shown.
The instruction at the sentencing hearing was in conformity with the law as stated in State v. Dixon, 283 So.2d 1 (Fla. 1973), cert. denied, 416 U.S. 943, 94 S.Ct. 1951, 40 L.Ed.2d 295 (1974). The death penalty is appropriate where there exists evidence of one or more aggravating circumstances proved by the state beyond a reasonable doubt. Mitigating circumstances are not offered as rebuttal evidence of aggravating *1389 circumstances. Mitigating circumstances, if any, are offered by the defendant to show that the "totality of the circumstances" warrants less than the death penalty. There is no improper "shifting" of the burden of persuasion with respect to a fact which must be proved during the sentencing procedure.
The trial court's instruction, when considered in its entirety, was a proper admonishment to the jury that they were not to add up the aggravating and mitigating factors in a mechanistic and wooden fashion, but were to weigh the "totality of the circumstances" in arriving at a reasoned judgment as to whether the facts warranted imposition of the death penalty or life imprisonment. The court instructed the jury that should mitigating circumstances outweigh the presumed fact, they were not bound by the presumption.
The instruction of the trial court was not improper, so the failure of counsel to challenge the instruction on direct appeal did not deprive defendant of effective assistance of appellate counsel.
Having now carefully considered the alleged ineffectiveness of appellate representation, we find no serious deficiencies causing prejudices to defendant. The petition for writ of habeas corpus is denied.
It is so ordered.
ALDERMAN, C.J., and BOYD, OVERTON and McDONALD, JJ., concur.
