Freezer burn is beef's worst enemy. It affects the taste, appearance and smell of all beef products, including tenderloin. When improperly wrapped or refrozen, the meat loses a large amount of surface moisture which causes the burn. To prevent your tenderloin from burning in the freezer, you must properly wrap it, freeze it quickly and use it in a timely manner. As hearty a meat as beef is, it is delicate and fickle if not properly stored and cared for.
Leave the tenderloin in its original packaging if possible, and wrap thoroughly in plastic cling wrap.
Place the wrapped beef inside of a freezer zip locking bag, and squeeze out all of the air.
Place the bag inside of a snap-locking plastic container.
Place the container of beef in the freezer to freeze the tenderloin as quickly as possible. Beef's freezing point is 28 degrees Fahrenheit rather than 32, so the colder you can get your freezer, the better. Rapid freezing causes less damage to the beef than slow freezing, therefore a deep freezer that can reach zero degrees Fahrenheit or close to it is best. If your freezer cannot reach that low, set it to the lowest degree possible granted it doesn't jeopardize anything else in the freezer.
Let the beef rest in the freezer for no more than two weeks. Frozen beef tenderloin is best if it is thawed and consumed after no more than two weeks in the freezer. While you can still eat it after three to four weeks, it is at its best under two.