Making magic squares with side length multiple of four

Magic squares whose side length is a multiple of four can be easily created using the following steps:

1. Mark the cells that belong to the diagonal of all 4 by 4 sub-squares.
2. Starting from the upper right corner, count each cell, writing the number counted if the cell has been marked.
3. Starting from the lower left corner, count each cell, writing the number counted if the cell is empty.

If we apply the steps mentioned above to a 4 by 4 square, we first mark the cell located on the diagonals.

Then we fill the marked cells by counting from the upper right cell.

Finally we fill the unmarked cells by counting from the lower left cell.

The result is a 4 by 4 magic square. The sum of the numbers in each row, each column and each diagonal is equal to 34.