Remove Silverskin

Pork, beef, and lamb tenderloins all have an area of connective tissue known as silverskin for its silvery-white appearance. Silverskin doesn't dissolve when the tenderloin is cooked, so it needs to be trimmed away.

Position the tip of a boning knife about 1/2 to 1 inch from one end of the visible silverskin. Push the tip under a strip of silverskin about 1/2 to 3/4 inch wide. Angle the knife slightly up toward the silverskin as you slide the knife down the tenderloin, freeing the silverskin. Use your free hand to hold the silverskin taut as you cut. If your knife isn't extremely sharp, you may need to use a slight sawing motion to work down the tenderloin. Once you've cut all the way through the end of the strip, turn the knife around and cut off the end that's still attached. Repeat until all the silverskin is gone.

http://www.finecooking.com/articles/how-to-trim-tenderloin.aspx