Let us take a look at the following magic square of order n=4. You can easily see that this square is pandiagonal, as all rows, columns and diagonals sum to S=65.

1

15

22

18

9

23

19

6

5

12

10

2

13

24

16

14

21

20

7

3

17

8

4

11

25

25

11

4

8

17

3

7

20

21

14

16

24

13

2

10

12

5

6

19

23

9

18

22

15

1

Now we transform this magic square into its complement and we can see that a rotation with an angle of 180° will produce the original square again. So it is selfcomplement and hence ultramagic.