The umbilical cord should be exposed to the air for drying. Diapers should be kept below the cord. Let the cord dry up naturally. It is ok to clean the area with warm water or with an alcohol swab, although this is not necessary. It usually falls off in three weeks or less. Continue cleaning the cord area for one week after the cord falls off.
Though a small amount of bleeding or white discharge isn’t unusual or cause for alarm, excess amounts of bleeding, redness around the umbilical cord stump, or presence of pus should be reported to your baby’s health care provider.