Decide who will keep the property and continue to make payments on the mortgage. The party in the best financial position to hold the mortgage on their own is the wisest choice.
Apply for a new mortgage. The person who will be keeping the mortgaged property must apply for, and be approved for, a new mortgage based on sole income. In the case of divorce, any child support and alimony paid to the person keeping the property is often considered as claimable income.
Request a letter of release. If the new application is approved, the person wishing to have their name removed from the mortgage can request a letter of release from their mortgage holder. They are no longer responsible for mortgage payments under the terms of the new mortgage agreement.
Implement plan "B," if necessary. Should the new mortgage application be denied, both parties must agree to sell the home and pay off the mortgage in full. This will satisfy the bank loan and remove both person's name from the now fully-paid mortgage.