The original square? what do you mean by that?
1) That the first, non-rotated picture is there, in the background? or
2) That the background is a solid color (usually it may be white, but some rotating programs (like IrfanView) allow you to make that background any one color you want. or
3) That you expect that the angular sides to be the end of any image area?
If the answer is #3, then that is sort of harder (not impossible) to do, since images on computers typically have straight horizontal and vertical edges. One easy way of getting what you want, if that is #3, is to make the unwanted, "islanded," triangular corners an invisible color. You can make a color invisible with tools that save in either the GIF or PNG format.
I am making my own CD/DVD covers using photos from my collection. I have been trying to tilt a photo to give a different effect, unfortunately I have tried many photo programmes with the same result. First I can tilt the photo e.g. 10 degrees left or right, but when I save the photo I am left with the photo ok but with the original square as a background, I cannot seem to find a way to remove this. I would appreciate any help please. I have Photoshop which doesn't seem to solve my problem.