You don't cut the corners off and reuse them, you take one of the 4-1/2" squares, draw a diagonal line (for instance: from upper left corner to lower right corner) from one corner to the oposite diagonal corner. Repeat for ALL 4-1/2" squares...I use a regular, cheapo mechanical pencil for this. Mark lightly. If it's too dark of a fabric, get a white colored pencil, or fabric marker.
Next, lay one of the 4-1/2" squares onto the corner of the 8-1/2" square, matching the edges exactly.
Sew exactly on the drawn line. You can then cut off the extra on the corner, leaving a 1/4" seam allowance. Repeat for the other corners.
HINT: Instead of just tossing the cut off parts of the corners, I first do a 2nd line of stitching 1/2" from the first (toward the corner edge)...then cut the edge piece off, leaving 1/4" seam allowance...you get an automatic half square triangle you can use elsewhere.