The IRS does allow divorced parents to release a claim for dependent children by filing form 8332.

However, the child will be treated as the qualifying child of the noncustodial parent if the special rule for children of divorced or separated parents (or parents who live apart) applies. See Publication 504, Divorced or Separated Individuals, for more information. This rule requires in part, that both of the following conditions are met:

The custodial parent signs a Form 8332, Release/Revocation of Release of Claim to Exemption for Child by Custodial Parent, or a substantially similar statement, and The noncustodial parent attaches the Form 8332 or a similar statement to his or her return. If the custodial parent releases a claim to exemption for a child, the noncustodial parent may claim the child as a dependent and as a qualifying child for the child tax credit. However, generally, the noncustodial parent may not claim head of household filing status or the earned income credit, and the noncustodial parent may not claim the credit for child and dependent care expenses, the exclusion for dependent care benefits, or the health coverage tax credit.IRS rules for parents who give exemption to divorced partner.