
279 So.2d 885 (1973)
The TRAVELERS INSURANCE CO., Appellant,
v.
Philip A. LUCKETT, Appellee.
Nos. 72-1204 and 72-1248.
District Court of Appeal of Florida, Third District.
June 19, 1973.
Rehearing Denied July 23, 1973.
Adams, George & Wood, and David L. Willing, Miami, for appellant.
Michael L. Lipsky, Miami, for appellee.
Before BARKDULL, C.J., and PEARSON and HENDRY, JJ.
HENDRY, Judge.
In these consolidated appeals appellant-plaintiff insurance company seeks review of an adverse final judgment entered in an action for declaratory relief and an award of attorney's fee therein. Appellant sought a declaration of its liability to appellee-defendant under an uninsured motorist provision of an automobile liability policy issued by it to appellee.
Appellee insured was involved in an automobile accident with an uninsured motorist while covered by two separate insurance policies, one issued by appellant and one issued by Midwest Mutual Insurance Company. Both policies contained arbitration clauses in the event of a dispute as to claimed damages or liability of the uninsured motorist.[1] Appellee filed a claim for damages with Midwest Mutual which resulted in appellee receiving a $3,750.00 arbitration award that was paid and satisfied. Appellee then asserted a claim for *886 arbitration to assess his damages against appellant, Traveler's Insurance Company, for the same injuries arising out of the same accident.
Appellant, Traveler's, instituted this action to have its rights declared as against appellee's claim and requesting that appellee be enjoined from prosecuting his claim under the policy. As grounds therefor, appellant alleged that the appellee was estopped[2] from asserting his claim due to the effect of the prior arbitration and satisfaction arising therefrom. The trial court disagreed and dismissed the action and allowed appellee to continue prosecuting his claim. We reverse.
The issue before us is the effect to be given to the first arbitration's determination of appellee's damages of $3,750.00, and whether appellee can attempt to gain a second, hopefully greater, determination of his damages under the second arbitration.[3]
It has long been established in this state that a valid agreement to arbitrate the amount of damages between an insured and insurer, and a subsequent award based thereon is binding on the parties. Hanover Fire Ins. Co. v. Lewis, 28 Fla. 209, 10 So. 297; American Fidelity Fire Ins. Co. v. Richardson, Fla.App. 1966, 189 So.2d 486; Bohlmann v. Allstate Ins. Co., Fla.App. 1965, 171 So.2d 23. Moreover, such an agreement to arbitrate is governed by the provisions of the Florida Arbitration Code[4] and the procedures for challenging the propriety or regularity of the award or proceedings are set out specifically therein.[5] Netherlands Ins. Co. v. Moore, Fla.App. 1966, 190 So.2d 191; Hall v. Nationwide Mutual Ins. Co., Fla.App. 1966, 189 So.2d 224; Bohlmann v. Allstate Ins. Co., supra; Cruger v. Allstate Ins. Co., Fla.App. 1964, 162 So.2d 690.
In the case sub judice, appellee does not believe that the initial factual determination of his damages was correct or sufficient. He, thus, attempts to acquire a second determination of his damages under the arbitration clause of appellant's policy. The very essence of an arbitration is an agreement to be bound by the factual determination of the arbitrator and thus end the factual controversy. Bankers & Shippers Ins. Co. v. Gonzalez, Fla.App. 1970, 234 So.2d 693. Thus, appellee would not have been entitled to challenge the factual nature of the damage award after the first *887 arbitration.[6] He attempts here to indirectly challenge that finding. It is well established that a party may not do indirectly what he is forbidden to do directly. Cf., Bankers & Shippers Ins. Co. v. Gonzalez, supra. We are, therefore, of the opinion that the chancellor erred in finding that the appellee was entitled to a second chance to establish his damages for this accident.
The appellee has directed our attention to the following wording in the case of Sellers v. United States Fidelity & Guaranty Co., Fla. 1966, 185 So.2d 689, 692, in support of his contention that he is entitled to pursue his claim against appellant:
"[4] By the foregoing paragraph we do not mean to imply that an insured protected by multiple policies issued under § 627.0851 shall be delayed or frustrated in effecting settlement by having to pursue his claim of loss against all of the insurers jointly. He can proceed against any one or more of them, but in any event he shall not be entitled to recover from all of them more than the amount of his loss from bodily injury caused by an uninsured motorist and, of course, his recovery from any one of them shall be within the limit of the particular policy. No doubt each insurer will properly insist that the insured inform it of the total amount of his loss and whether or not he has other similar insurance and whether any settlement has been reached with another insurer before settling a claim. As a practical matter when settlement or recovery of the loss between insured and insurer is effected it will then be in order for the insurers to make pro-ration inter se."
Accord, Allstate Ins. Co. v. Dairyland Ins. Co., Fla. 1972, 271 So.2d 457. We find no support for appellee's position within these cases for they do not deal with the issue before us  whether the insured is entitled to a second arbitration to again determine his damages for the same accident. The quotation solely establishes the right of a claimant to seek a full satisfaction from one or more insurance carriers based on a finding of damages that may or may not be covered under one or more policy limits. It does not in any way establish the right of a claimant to seek a new determination of his damages arising from the same accident for each insurance policy that affords possible coverage. The issue of a pro-ration between the respective insurers is not the issue before us, as it was in the Sellers and Dairyland cases, supra.
Accordingly, the final judgment appealed from and the attorney's fee award entered therein is hereby reversed and remanded with directions for the trial court to enter judgment in favor of the appellant.
Reversed and remanded with directions.
NOTES
[1]  Appellant's policy provided for arbitration in accordance with the rules and regulations of the American Arbitration Association. Midwest Mutual's policy provided for private arbitration since it is not a member of the American Arbitration Association.
[2]  Appellant also alleged in its complaint that the doctrine of res judicata would hold them harmless from appellee's claim. The record reveals that the parties stipulated, at hearing, that the issue of res judicata was inapplicable and it was never considered further.
[3]  Appellee has submitted that he seeks only one full award and admits that in the event the second arbitration results in a finding less than already awarded, then he would be entitled to nothing on his claim from appellant.
[4]  Ch. 682, Fla. Stat., F.S.A.
[5]  § 682.13(1), Fla. Stat., F.S.A. provides for the following specific grounds for vacating an arbitration award:

"(a) The award was procured by corruption, fraud or other undue means;
"(b) There was evident partiality by an arbitrator appointed as a neutral or corruption in any of the arbitrators or umpire or misconduct prejudicing the rights of any party;
"(c) The arbitrators or the umpire in the course of his jurisdiction exceeded their powers;
"(d) The arbitrators or the umpire in the course of his jurisdiction refused to postpone the hearing upon sufficient cause being shown therefor or refused to hear evidence material to the controversy or otherwise so conducted the hearing, contrary to the provisions of § 682.06, as to prejudice substantially the rights of a party; or
"(e) There was no agreement or provision for arbitration subject to this law, unless the matter was determined in proceedings under § 682.03 and unless the party participated in the arbitration hearing without raising the objection;
"But the fact that the relief was such that it could not or would not be granted by a court of law or equity is not ground for vacating or refusing to confirm the award." (Emphasis supplied.)
[6]  See emphasized portion of § 682.13(1)(e), Id.; Bankers & Shippers Ins. Co. v. Gonzalez, Fla.App. 1970, 234 So.2d 693.
