Remove the screws that secure the door handles together using the Allen wrench.
Pull the door handles off of the cylinder shaft.
Pry off the retaining clip at the end of the cylinder shaft with the flat-head screwdriver. Take off the clip and set it aside for use later.
Pull the cylinder straight out of the locking mechanism.
Turn the cylinder 180 degrees and reinsert it into the locking mechanism.
Reattach the retaining clip onto the end of the cylinder shaft. Press on the clip to secure it in place.
Place the door handles back on the cylinder shaft and tighten the screws with the Allen wrench.