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. This part brings magic squares of orders 36 and 40. For the previous orders from order 8 to 32 click the two links (link1, link2). Whole the work with pdf files can be accessed at the author's site (order 36, order 40). 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.