Article: Set them aside for later. Cut nearly to the bottom of the threshold, but do not cut all the way through to avoid cutting the toe kick.  If any section is not coming free easily, use a hammer and chisel to break it into pieces before prying it up. Cut the new threshold to fit with a circular saw if necessary.  Allow it to dry.  This will prevent the threshold from cracking as you drive in the new nails.
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Remove the door casings on either side of the doorway. Insert the end of a pry bar behind the casings and gently tug them free. Use a circular saw to cut the threshold into three pieces. Cut the rest of the way through the threshold with a handsaw for control. Insert a pry bar beneath each section of the threshold and pull it free. Measure the length of the door sill and ensure that the new threshold is of equal size. Slide the new threshold into place to ensure that it fits. Paint the new threshold with a water and UV proof stain to help protect it from the elements. Slide the new threshold back into place. Drill pilot holes into the threshold that are slightly smaller than the finish nails that will hold it in place. Hammer in the finish nails to hold the threshold in place. Fill the nail holes with wood putty. Reattach the casings on either side of the doorway. Hammer the finish nails back into place to reinstall the casings.