How to Hide the message Icon from my Facebook profile page from people who are not my friend

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How do I remove the messaging option from my Facebook profile page? The messaging link that is next to the friend request link on the page of every Facebook user, how does one remove the messaging link from ones own Facebook profile? To keep people who are not on you're friends list from messaging you.

See: How do I deactivate Facebook Account

How to Hide the message Icon from my Facebook profile page from people who aren't my friend

Unfortunately, this feature has been removed recently. Those who had it set to "no messaging" prior to the change will still continue to not have a "Message" button, but now the only options are "Basic" or "Strict" filtering, which can be found in Settings (the 'down' arrow on the upper dark blue band, next to the lock symbol will have a drop-down menu) and then "Privacy" in the left hand side menu > "Who can contact me?", then "Whose messages do I want filtered into my Inbox?"