
687 So.2d 860 (1997)
Darrell Ashton CHATMAN, Appellant,
v.
STATE of Florida, Appellee.
No. 94-1345.
District Court of Appeal of Florida, First District.
January 16, 1997.
*861 James T. Miller of Corse, Bell & Miller, P.A., Jacksonville, for Appellant.
Robert A. Butterworth, Attorney General; Amelia L. Beisner, Assistant Attorney General, Tallahassee, for Appellee.
WEBSTER, Judge.
In this direct criminal appeal, appellant seeks review of his conviction for robbery. He claims that the trial court committed reversible error when it prevented him from questioning on cross-examination a state witness who claimed to have participated in the robbery, regarding representations allegedly made by law enforcement to induce him to give statements implicating appellant. We agree and, accordingly, reverse.
Early on the morning of September 29, 1993, a bank teller, accompanied by a guard, was robbed of two bank pouches (which contained no money) while on her way to a side building that housed the drive-in tellers. The guard was able to say only that the robbers were three people dressed in black, and that at least one carried a gun. The teller believed the three to have been males, and added that one had on a tee shirt that had some white in it. The guard fired six shots at the robbers, all of whom ran off.
Police arrived within minutes. The first to arrive broadcast a BOLO for three (or, depending on whom is believed, four) black males, dressed in black. Another officer saw three black males, dressed "[b]asically all in dark clothing," who "appeared to be out of breath like they had been running," a short distance from the bank. When the officer attempted to stop them, "they took off running." Eventually, appellant and Eald Walker were apprehended. Appellant had on dark blue clothes, and Walker was wearing a white tee shirt and black pants. Neither appellant nor Walker had either the bank pouches or a gun when arrested.
On the day of the arrests, Walker was interrogated, and eventually gave statements implicating appellant. An information was filed, charging both appellant and Walker with armed robbery. However, Walker subsequently worked out a deal with the state, pursuant to which he agreed to plead guilty to the armed robbery and to admit a violation of probation, and to testify against appellant, in return for a sentence of 4½ to 5½ years in prison, subject to a 3-year mandatory minimum term.
At trial, after Walker had testified on direct examination, implicating appellant in the robbery, appellant's attorney pursued a line of questions regarding Walker's interrogation by law enforcement following his arrest. Walker testified that he had been interrogated by both a police detective and an FBI agent. He said that they wanted him to give a statement. He also said that he ultimately did give statements, and that part of his motivation for doing so was what the detective and the FBI agent had said to him. However, when appellant's attorney asked what the law enforcement officers had said, *862 the state objected that the question called for hearsay. Appellant's counsel responded that the question did not seek hearsay because the statements made by the law enforcement officers were not being offered to prove the truth of the matters asserted but, rather, they were being offered to establish a motive for Walker falsely to implicate appellant in the robbery, and to show bias toward appellant on Walker's part. The trial court sustained the state's objection, holding that the statements would be hearsay and that, even if they qualified under some exception to the hearsay rule, they were not relevant to any material issue. Appellant was found guilty by the jury of unarmed robbery, and this appeal follows.
At trial, appellant's attorney told the trial court that, if permitted to answer, Walker would testify (1) that the detective had told him that appellant had already confessed, implicating him (which statement was, according to appellant's attorney, false); and (2) that the FBI agent promised him that, if he gave a satisfactory statement, he would not be prosecuted on the federal charge of bank robbery. According to appellant's attorney, Walker would also testify that both of those representations had an effect on his decision to give statements. The state did not contest in the trial court the accuracy of the assertions made by appellant's attorney, and does not do so here. Moreover, on appeal, the state concedes that the testimony would not have been hearsay. However, it maintains that it was properly excluded because it was not relevant to any material issue. In the alternative, the state argues that any error in excluding the testimony was harmless.
We agree with appellant that the testimony sought to be elicited from Walker regarding statements made by the detective and the FBI agent was not hearsay, because it was not being "offered ... to prove the truth of the matter asserted." Fla.Evid. Code § 90.801(1)(c). As we have said in the past:
Section 90.801(1)(c), Florida Statutes, defines "[h]earsay" as "a statement, other than one made by the declarant while testifying at the trial or hearing, offered in evidence to prove the truth of the matter asserted" (emphasis added). Thus, "[o]ut-of-court statements constitute hearsay only when offered in evidence to prove the truth of the matter asserted." Anderson v. United States, 417 U.S. 211, 219, 94 S.Ct. 2253, 2260, 41 L.Ed.2d 20, 28-29 (1974). "The prohibition of the hearsay rule ... does not apply to all words or utterances merely as such.... The hearsay rule excludes extra-judicial utterances only when offered for a special purpose, namely, as assertions to evidence the truth of the matter asserted." 6 Wigmore, Evidence § 1766, at 251 (Chadbourn rev. 1976).
Fields v. State, 608 So.2d 899, 903 (Fla. 1st DCA 1992). As Professor Ehrhardt has expressed it, "If an out-of-court statement is offered in court to prove the truth of the facts contained in the statement, it is hearsay. If an out-of-court statement is not offered to prove the facts contained in the statement, it is not hearsay." Charles W. Ehrhardt, Florida Evidence § 801.2 at 556-57 (1996 ed.) (footnotes omitted). Clearly, here, the testimony regarding statements made by the detective and the FBI agent was offered to show what Walker's state of mind was at the time he made the statements implicating appellant and, thereby, to establish a motive why Walker might falsely implicate appellantin other words, to suggest a reason why Walker might have been biased against appellant at the time that he made the statements.
We also agree with appellant that the testimony was relevant to a material issue. "Bias or prejudice of a witness has an important bearing on his credibility, and evidence tending to show such bias is relevant." Webb v. State, 336 So.2d 416, 418 (Fla. 2d DCA 1976). "The courts have repeatedly held that a defendant has the right to fully crossexamine a State's witness to reveal bias and any improper motive the witness may have had in testifying against the defendant." Powe v. State, 413 So.2d 1272, 1273 (Fla. 1st DCA 1982). In Taylor v. State, 623 So.2d 832 (Fla. 4th DCA 1993), a case involving a substantively similar issue, the court held that the defendant should have been permitted *863 to question a former co-defendant who had implicated the defendant regarding his motive to testify falsely about the defendant's participation. The court said, "It is, of course, clear that a defendant in a criminal case has a constitutional right to a full and fair cross-examination of his accuser. Especially is this true if a key state witness is the subject of the cross-examination." Id. at 833.
We hold that it was error to preclude appellant from questioning Walker regarding the statements made to him by the detective and the FBI agent. We agree with the state that the error was harmless as to the statement made by the FBI agent, because appellant's attorney was able to elicit testimony from Walker that his statements were motivated in part by the belief that he would not be prosecuted in federal court for bank robbery if he gave a satisfactory statement. However, nothing regarding the detective's statement that appellant had already confessed, implicating Walker, or Walker's reaction to that statement, was heard by the jury. The state argues that this latter error was harmless because "there was plenty of other evidence showing that the two men had committed the crime together."
We are unable to accept the state's harmless error argument regarding the detective's statement. It is true that there was some other evidence linking appellant to the crime. However, other than Walker, there was nothing to implicate appellant in the actual commission of the robbery. Rather, the only other evidence was that appellant was in the immediate vicinity of the robbery, with two other males, minutes after it had taken place; that he appeared to have been out of breath; that he had on dark clothes; and that he ran when confronted by police. Given the nature of the evidence presented at trial, we are not able to "say beyond a reasonable doubt that the error did not affect the verdict." State v. DiGuilio, 491 So.2d 1129, 1139 (Fla.1986). See Taylor v. State, 623 So.2d 832 (Fla. 4th DCA 1993) (error in refusing to permit crossexamination of former co-defendant to establish motive falsely to implicate defendant not harmless in light of paucity of other evidence incriminating defendant).
In summary, we hold that it was error to preclude appellant from questioning his former co-defendant regarding statements made by the detective and the FBI agent who interrogated the co-defendant, in an effort to establish that the co-defendant had a motive falsely to implicate appellant in the robbery. We hold, further, that, although exclusion of testimony regarding the FBI agent's statement was harmless under the circumstances, exclusion of testimony regarding the detective's statement was not. Accordingly, we reverse, and remand for a new trial.
REVERSED and REMANDED, with directions.
MINER, J., concurs.
LAWRENCE, J., concurs in result only.
