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I had EAD, but didn't renew it. So i don't have personel experience about renewal but i saw few came directly to the Newarkoffice for renewal while i went first for applying EAD.
I guess the procedure willbe more or less same as applying EAD, might be processing time could be less.
Check this link:
EAD Renewal Paper Filing questions - Immigration Voice
You need to fill I-765( http://www.uscis.gov/files/form/I-765.pdf) form, mention details of you previous EAD like where issued, etc.,
While submitting documents, you need to submit front and back copy of your previous EAD. This is what i understand from my search after reading your post.
If i get to know more, let me share it.
For more information, better go through this USCIS site too: