Self-complementary magic squares of doubly even orders

Abstract A magic square M in which the entries consist of consecutive integers from 1 , 2 , … , n 2 is said to be self-complementary of order n if the resulting square obtained from M by replacing each entry i by n 2 + 1 − i is equivalent to M (under rotation or reflection). We present a new construction for self-complementary magic squares of order n for each n ≥ 4 , where n is a multiple of 4 .