24 hour notation incorrect starting at midnight

I use the 24 hour notation digital clock on my watch face and I recently saw that it was the incorrect notation starting at midnight till 1 am. The expected notation would have been 00:00 till 00:59, but it was 24:00 till 24:59. That is of course not correct. On a 24 hour clock, the time resets at midnight and starts over at 00:00.