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In addition to Facebook Pages being able to update a Twitter account, Facebook now lets individuals (that means you!) do the same as well.
See the full article by Emil Protalinski here: Facebook now lets you update Twitter.
Go to <a href="http://www.facebook.com/twitter/">facebook.com/twitter</a> and click the green button titled "Link My Profile to Twitter."
You'll be redirected to Twitter temporarily. Click the blue button titled "Authorize app."