We prove that there exists a pair of orthogonal diagonal Latin squares of order v with missing subsquares of side n (ODLS( v, n)) for all v ⩾ 3 n + 2 and v − n even. Further, there exists a magic square of order v with missing subsquare of side n (MS( v, n)) for all v ⩾ 3 n + 2 and v − n even.