For the first time in history, this work brings a new kind of magic squares. These are multiples of 4 starting from order 8. These are two digits bordered magic squares based on magic rectangles of order 2x4. This part brings magic squares of orders 8, 12, 16, 20 and 24. The second part is for the orders 28 and 32. Whole the work with pdf files can be accessed at the author's site. The single digit bordered magic squares are already known in the literature. For three digits, we work with magic squares of order 3. For four digits we work with magic squares of order 4.