That's debatable ;) I've seen arguments each way. Here's one from greenwichmeantime.com:

AM and PM start immediately after Midnight and Noon (Midday) respectively.

This means that 00:00 AM or 00:00 PM (or 12:00 AM and 12:00 PM) have no meaning.

Every day starts precisely at midnight and AM starts immediately after that point in time e.g. 00:00:01 AM (see also leap seconds)

To avoid confusion timetables, when scheduling around midnight, prefer to use either 23:59 or 00:01 to avoid confusion as to which day is being referred to.

It is after Noon that PM starts e.g. 00:00:01 PM (12:00:01)