The stump of the umbilical cord usually dries out and falls off in a week or two, but has been known to stay on for up to a month. Keep the area where the cord is attached to the baby clean and dry to prevent infection. It does not need to be cleaned with alcohol and should be left open (do not cover it with the diaper). Air is good to dry out the cord. Call your doctor if the area around the cord is red, swollen or you notice an unusual smell or discharge.