It's been a week of weird finds for the Transportation Security Administration: A six-pack of nunchucks and other sharp objects -- and now a dog in a backpack.

“A dog was accidentally sent through the X-ray” at the Dane County Regional Airport in Madison, Wisconsin this week, the TSA said on its verified Great Lakes region Twitter account on Tuesday afternoon.

Animals need to be removed from carrying cases and the empty carrier sent through the screening machine, the TSA said.

“When traveling with any animal, notify your airline & know their rules,” the agency said in its tweet.

This latest discovery comes after last month's find of a live cat trapped inside a suitcase at John F. Kennedy Airport in New York.

That cat -- with the unforgettable name of Smells -- was treated to a human-sized Thanksgiving feast after his ordeal.

Flying with a pet

Major airlines in the United States charge fees for traveling with a pet on board a flight -- sometimes in excess of the cost of airfare itself.

American Airlines and United Airlines charge $125 one-way. Southwest and Delta charge $95 one-way.

If you want to travel with your small pet in the cabin of a plane, TSA has some helpful hints so you can do it the correct and humane way. (CNN)

•PHOTO:The Transportation Security Administration found this adorable Chihuahua in a passenger's checked luggage at LaGuardia Airport in Queens, New York, on Tuesday, December 7.