
766 So.2d 313 (2000)
Douglas LOGUE, Appellant,
v.
Barbara A. LOGUE, Appellee.
No. 4D98-2563.
District Court of Appeal of Florida, Fourth District.
March 1, 2000.
*314 M. Annette Himmelbaum, Miami Beach, for appellant.
No brief filed for appellee.
KREEGER, JUDITH, L., Associate Judge.
The Logues were divorced by final judgment entered on February 12, 1998. The final judgment granted custody of their son, Brandon, to Mr. Logue and their son, Johnathan, to Ms. Logue. While Mr. Logue's appeal from the final judgment was pending, Mr. Logue filed a motion for rehearing and for a stay, and he refused to send Johnathan to Ms. Logue. Until the trial court specifically ordered him to send Johnathan to Ms. Logue, he did not pay to Ms. Logue his share of the ordered child support for Johnathan. On Ms. Logue's motion, the trial court found him in contempt for failure to make those payments,[1] and granted Ms. Logue attorneys' fees in the amount of $2,476.25. Mr. Logue appeals that order. During the pendency of the appeal he also filed a motion for relief from judgment contending that the court made a mathematical error in calculating child support. The trial court denied relief on the ground that it lacked jurisdiction because of the pendency of the appeal of the final judgment. This court affirmed the original final judgment without opinion, so it did not specifically address the mathematical error in the judgment. Mr. Logue appeals the denial of the motion for relief from judgment.
Mr. Logue contends the trial court erred in computing his child support obligation, according to the guidelines. Ordinarily this court could not revisit in this appeal an issue determined in the final judgment which has now become the law of the case. Bueno v. Khawly, 677 So.2d 3 (Fla. 3d DCA 1996). However, if the final judgment contained an error that was manifestly unjust, then this court may now rectify that mistake. Jacobson v. Humana *315 Med. Plan, 636 So.2d 120 (Fla. 3d DCA 1994); McDonough Power Equip. Co. v. Brown, 486 So.2d 609 (Fla. 4th DCA 1986). This is a seldom used but important appellate power. "Exceptions to the doctrine [of the law of the case] should be invoked only `in unusual circumstances and for the most cogent reasonsand always, of course, only where "manifest injustice" will result from a strict and rigid adherence to the rule.'" White Sands, Inc. v. Sea Club Condo. Ass'n, 591 So.2d 286, 288 (Fla. 2d DCA 1991) (quoting Strazzulla v. Hendrick, 177 So.2d 1, 4 (Fla.1965)), and (quoting Beverly Beach Properties v. Nelson, 68 So.2d 604 (Fla.1953)).
In its final judgment, the trial court relied on the methodology used by Judge Altenbernd in Winters v. Katseralis, 623 So.2d 613 (Fla. 2d DCA 1993) for calculating child support in cases where custody of children of the marriage is divided between the parents.[2] However, interestingly enough, Judge Altenbernd professed his lack of mathematical prowess in Gingola v. Velasco, 668 So.2d 1054 (Fla. 2d DCA 1996), stating that in Winters he had omitted a necessary part of the equation. The trial judge in this case applied the Winters formula (citing to Winters in the judgment) without making the Gingola correction. Specifically, the trial judge found Mr. Logue's child support obligation was $780, and Ms. Logue's child support obligation was $85, and then the trial judge ordered that Mr. Logue pay Ms. Logue the difference, $695 monthly. However, in Gingola, Judge Altenbernd acknowledged that the parent who has the greater obligation should pay the other parent one-half of that difference, thus recognizing the obligation of each parent to contribute to the support of both children. The trial judge neglected to make that adjustment, an error of $347.50 monthly. For Mr. Logue, who according to the trial judge, then earned $2,314 and who has custody of one of their children, that difference in his ongoing monthly support obligation is substantial enough to constitute manifest injustice.
Because of the manifest and continuing injustice which would occur should we let this mathematical mistake go uncorrected, we reverse the denial of the motion for relief from judgment so that the trial court can make the proper correction of the final judgment on remand. We also reverse the order of contempt as the revision of the amount of child support in the final judgment will reduced the amount due and owing pursuant to the final judgment.
Mr. Logue also contends he should not be obligated to pay any child support to Ms. Logue while he disobeyed the final judgment by withholding Johnathan from her for the period from the entry of the final judgment until he sent Johnathan to Ms. Logue. The trial court considered and rejected that argument and we find this not to be an abuse of discretion or an error of law. Mr. Logue's argument is similar to that of the child who kills his or her parents, then begs the court for mercy because the child is now an orphan.
All other grounds asserted for this appeal by Mr. Logue are without merit.
For the above reasons, we reverse the order of contempt and remand this case to the trial court for further proceedings in accordance with this opinion.
REVERSE AND REMANDED.
WARNER, C.J., and STEVENSON, J., concur.
NOTES
[1]  The arrearage was from the date of entry of the final judgment until Mr. Logue actually sent Johnathan to Ms. Logue (February 12, 1998, until May 7, 1998), and totals $2,246.
[2]  In Winters, each parent had custody of one of their two minor children.
