The Strachey method for magic squares is an algorithm for generating magic squares of singly even order 4k + 2.
An example of magic square of order 6 constructed with the Strachey method: Strachey's method of construction of singly even magic square of order n = 4k + 2.
Divide the grid into 4 quarters each having n2/4 cells and name them crosswise thus 2.
Using the Siamese method (De la Loubère method) complete the individual magic squares of odd order 2k + 1 in subsquares A, B, C, D, first filling up the sub-square A with the numbers 1 to n2/4, then the sub-square B with the numbers n2/4 + 1 to 2n2/4,then the sub-square C with the numbers 2n2/4 + 1 to 3n2/4, then the sub-square D with the numbers 3n2/4 + 1 to n2.
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 n=4k + 2.