In this paper, we consider magic squares which contain arithmeticprogressions. Mainly, we consider the magic squares similar to Schaefer's 7-squares. We show how to construct magic squares of order 4k+3 which areof strict Schaefer's type. In general, it is unkown how to construct magicsquares of order 4k+1 which are of the type. However, we succeeded inconstructing magic squares of orders 9 and 13 which are of the type. At theend of this paper, we show an irregular pandiagonal magic 7-square of newclass.