Private Note Email Issue

Content

When our agents are adding private notes email type when they send the contact is getting an email also the Incident Unresolved message template.  This email to the contact does not have the private note of course but need for them to not even get an email when a private note email is added, only the agent should get the private note email.  We are using this unresolved message template so I cannot uncheck the send box in message templates.  Any thoughts how to not have this email go out to contacts when a private note email is added and sent?