Ending "friendships" on Facebook are a lot easier and less stressful than ending a friendship in real life. Just a click or two and the person is out of your life (at least on Facebook).
While the person won’t get a notice that you have "revoked" your friendship on Facebook, they might possibly get Friend Suggestions or see your profile elsewhere on Facebook and choose to Friend you (again).
The quickest way to Unfriend someone is to go to their Profile Page, scroll down to the bottom of the left sidebar, and click the link that says Remove from Friends.

A pop-up window will appear confirming your choice. If you’re sure, click the Remove from Friends button and you have officially Unfriended someone.

Another way to Unfriend someone is through the Edit Friends link on the Account dropdown menu.

On the Friends page, be sure the All Connections tab is highlighted.

An alphabetical list of Friends appears. Find the Friend you want to Unfriend and place the cursor on the X on the right side. The phrase Remove Connection will appear. Click on the X.

A confirmation pop-up window will appear. If you’re sure, click the Remove button and you and the person are no longer friends...on Facebook. (And no, Jason did not remove his connection from Kelli. Jason and Kelli Krafsky are still Facebook Friends).

source: The Facebooking Couple (K. Jason & Kelli Krafsky), authors of Facebook and Your Marriage at FacebookAndYourMarriage.com.
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