Yes, but most people ignored it and celebrated the new millennium at the end of 1999 and beginning of 2000 anyway.
See this: https://en.wikipedia.org/wiki/Millennium#Debate_over_millennium_celebrations
It's quite interesting. For example Fidel Castro made sure that Cuba celebrated correctly at the end of year 2000. And the U.S. Naval Observatory, official timekeeper for the country, held a party for the new milennium then too.
If we were to redefine it I wonder what way we'd go. Make -1 the first year of the first century and go in consistent 100 year steps from there? Or just accept that the first century and the first millenium are a little shorter than a hundred or a thousand years respectively?