Select Video which you want to download and open it in a new Tab of Google Chrome.
Now make some changes in the URL of this Video.
Suppose the URL of this Video is
http://www.facebook.com/video
Change this URL to Mobile Version. For this purpose, Change www to m Now the URL become like this.
http://m.facebook.com/video
After Changing the URL press Enter key. Now the mobile version of Facebook is opened. Now play this video. Let it play minimum 5 to 10 seconds.
Then Right Click on this video and select "Save Video as..." from an opened menu.
Now downloading will be started.
