Cut out a small strip of lightweight card roughly two thirds of the length of your middle finger and wide enough to wrap around it.
Tape the card together along the long edges to create a hollow tube. Insert one of the handkerchiefs into the tube.
Place the tip of your right middle finger into the end of the tube and bend your finger forward to conceal the tube in your right palm.
Hold the corner of the remaining handkerchief between your right thumb and forefinger and run it through your empty left hand to show the audience that it is an ordinary handkerchief. Quickly transfer the tube to your left hand after doing this a few times and switch to holding the handkerchief between your left thumb and forefinger. Run it through your now empty right hand.
Hold the handkerchief in your right hand and carefully stuff it into the tube concealed in your left hand. As you stuff more of the handkerchief into the top of the tube, begin pulling the concealed handkerchief out of the bottom of the tube to create the illusion that it is changing color in your hand.
Insert your right middle finger into the top of the tube as you finish stuffing the handkerchief in. Carefully conceal the tube in your right palm as you move your hand away ready to pull the second handkerchief out of your left hand fully.
Pull the second handkerchief out of your left hand and show it to the audience, then open your left palm to show that it is empty. Repeat Step 4 to show that the new handkerchief is real.