Turn the rug over so that the right side is down on the floor. Roll the rug up starting from the curled edge. Leave the rug curled for a few hours or overnight. Unroll the rug and return it to its original position.
Moisten the curled edge of the rug with a damp sponge. Stretch it flat and place a heavy object on top. Leave the object in place until the rug dries.
Run a steam machine over the rug and pay particular attention to the curled edges. Let the rug dry completely. Follow the manufacturer's directions for the steamer to achieve the best results.
Cut an adhesive floor tile into two triangles, using a utility knife. Turn the rug over. Make the curled edge of the rug as flat as possible with the palm of your hand. Peel the backing off one adhesive tile triangle and stick it to the corner of the rug while it is flat. Repeat this process for other curled corners. Turn the rug right side up.
Place a sheet of aluminum foil on an ironing board. Place the curled section of the rug on top of the foil with right side down. Cover this area with a damp towel and press it with a hot iron. Leave the iron in each section of the curled edge for 15 seconds at a time. Lay the rug flat to dry.
Apply heat to the curled section of the rug with a blow dryer if you do not wish to iron it. Lift the curled area of the rug and apply heat to the wrong side until it uncurls. Lay it flat.
Place an absorbent towel under the curled corner. Pour hot water on the area. Let the rug dry completely. It is best to perform this process outside.