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Once the addendum has been drafted, send it to the other party. Let them review it for accuracy and completeness. Before the addendum is signed, both parties need to understand what they are agreeing to. If the other party has any questions or concerns about the addendum, negotiate an acceptable agreement and re-draft the addendum as necessary. To demonstrate both parties' assent to the addendum and its terms, you and the other party need to sign the agreement in order to execute it. Sign the agreement in the appropriate location in the signature block and date it. However, in some leases, the original document might define who needs to sign the agreement. For example, maybe only the landlord needs to sign the addendum or vice versa. If required, or agreed to, you can get the signatures notarized, which will help prove that each party did in fact sign the agreement. A notary is a licensed professional who will witness each party sign the agreement. At the end, the notary will put their stamp of approval on the document saying they swear they saw each party sign it. Once the addendum has been executed, it should be attached to the original lease. You can make copies for your records as well.

Summary:
Make sure each party agrees to the terms of the addendum. Get the signature of every party. Have the addendum notarized. Attach the addendum to the original lease document.