If something is catty-corner, or catty-cornered, it sits on the diagonal: across the square from you, not next door and not straight across the street. American, informal. Many people say kitty-corner instead; some older speakers say cater-corner. All of them mean the same thing, and none of them have anything to do with cats, though they sound as if they do. The older form was cater-corner, from a word related to four — think of the four corners of a square, then the line between opposite corners. People heard cater and reshaped it toward catty and kitty. You will not hear this much in British English; they would just say diagonally opposite.