Why? – Once you are logged in to GMail you are automatically signed in to Facebook when you access a facebook page.
Other sites that FaceBook supports – MySpace, Yahoo!, Vidoop, MyOpenId, Verisign PIP, etc.
Facebook enables this feature using OpenID.
1. Log in to your GMail account.
2. Go to FaceBook.com
3. Go to your account settings page:
4. Click on change for Linked Accounts
5. Select an account and click “Link Account”.
6. In the window that pops up, make sure that the correct Google account is being used to link to FaceBook.
You are done!