Let the square be ABCD, and A’,B’,C’,D’ the midpoints of the 4 sides. Join A’C’, B’D’ and let this 2 segments intersect at O.

Now we only place 4 squares first. Note that we can assume that each of the 4 smaller squares have at least 1 square covering it. It’s easily to show that the regions of the 4 squares cannot lie on A’C’ and B’D’, and the result follows immediately.