The Strachey method for magic squares is an algorithm for generating magic squares of singly even order 4n+2.
Example of magic square of order 6 constructed with the Strachey method:
Strachey's method of construction of singly even magic square of order k=4*n+2
1. Divide the grid into 4 quarters each having k^2/4 cells and name them crosswise thus
2. Using the Siamese method (De la Loubère method) complete the individual magic squares of odd order 2*n+1 in subsquares A, B, C, D, first filling up the sub-square A with the numbers 1 to k^2/4, then the sub-square B with the numbers k^2/4 +1 to 2*k^2/4,then the sub-square C with the numbers 2*k^2/4 +1 to 3*k^2/4, then the sub-square D with the numbers 3*k^2/4 +1 to k^2.
3. Exchange the leftmost n columns in sub-square A with the corresponding columns of sub-square D.
4. Exchange the rightmost n-1 columns in sub-square C with the corresponding columns of sub-square B.
5. Exchange the middle cell of the leftmost column of sub-square A with the corresponding cell of sub-square D. Exchange the central cell in sub-square A with the corresponding cell of sub-square D.
The result is a magic square of order k=4*n+2.