Self-complementary magic squares of doubly even orders

A magic square M in which the entries consist of consecutive integers from 1,2,…,n2 is said to be self-complementary of ordern if the resulting square obtained from M by replacing each entry i by n2+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.