When sending message, I receive message “This is an automatically generated Delivery Status Notification. Delivery to the following recipients failed”

Original title: Message from "*** Email address is removed for privacy ***" delivery failed

When sending message to a relation in Australia, I receive message "This is an automatically generated Delivery Status Notification.
 Delivery to the following recipients failed."

 This has been happening for a few months now, also cannot receive E-mails from same person.

    Reporting-MTA: dns;dub0-omc2-s19.dub0.hotmail.com

    Received-From-MTA: dns;DUB113-DS24

    Arrival-Date: Wed, 13 Nov 2013 12:10:27 -0800

    Final-Recipient: rfc822;*********@aanet.com.au

    Action: failed

    Status: 5.5.0

    Diagnostic-Code: smtp;550 Recipient address rejected: User unknown in local recipient table

Can anyone help.

After seeing others with similar problem and request for further information, so I have included this.