Strange Squares

Here's a classic mystery that I learned when I was young. I still think it's pretty neat.

To the right is an square measuring 8x8, or 64 little squares. Draw this square on a piece of graph paper and cut it along the blue lines shown. Then rearrange the square to form a rectangle like the one below.

There, wasn't that easy?

Wait, something's wrong... the rectangle measures 5x13, which is 65 little squares, not 64. Where did the extra square come from?