Disappearing Act

You see before you a grid containing 65 identical squares.
(Do the math: 13 x 5 = 65.)
Watch closely; I am going to make one of them disappear.

First, I cut the grid into four pieces along these lines.

Then, I separate the pieces like this.

Now, I rearrange the pieces like this.

And join them back together to form a square.

That leaves us with a grid containing 64 identical squares.
(Do the math: 8 x 8 = 64.)
The 65th square has vanished before your very eyes!
Did anyone ever tell you that you have very eyes?

Here it is!