Midnight is called 24:00 if used to mean the end of the day and 00:00 if used to mean the beginning of the day . For example , you would say `` Tuesday at 24:00 '' and `` Wednesday at 00:00 '' to mean the exact same time . Where convenient , the notation 24:00 may also be used to refer to midnight at the end of a given dateâ '' that is , 24:00 of some day is the same time as 00:00 of the following day .