in order to avoid confusions of the time of the day, we should add a 23:59 and 00:01 instead of 00:00
The NIST (National Institute of Standards and Technology) recommends to avoid 00:00.
Is midnight the end of a day or the beginning of a day?
When someone refers to "midnight tonight" or "midnight last night" the reference of time is obvious. However, if a date/time is referred to as "at midnight on Friday, October 20th" the intention could be either midnight the beginning of the day or midnight at the end of the day.
To avoid ambiguity, specification of an event as occurring on a particular day at 11:59 p.m. or 12:01 a.m. is a good idea, especially legal documents such as contracts and insurance policies. Another option would be to use 24-hour clock, using the designation of 0000 to refer to midnight at the beginning of a given day (or date) and 2400 to designate the end of a given day (or date).
You can look at the entire text at http://www.nist.gov/pml/div688/times.cfm