The following square of order 4 is magic with magic sum S=34.
1  2  15  16 
12  14  3  5 
13  7  10  4 
8  11  6  9 
Now each number z is replaced by its complement
which results in a new magic square.


Under certain conditions the resulting magic square will be a reflected or rotated copy of the original magic square. These squares are called selfcomplement or selfsimilar magic squares.