Evidence suggests that those schools which have always reported incidents are now reporting fewer because of a range of strategies, but that there are a hard core of schools where the issue remains unacknowledged.
Roy Jobson, Edinburgh's director of children and families, said: "We were the first authority to publish figures of reported incidents in 1999 and I am pleased to say that several other authorities in Scotland have now followed our lead."
Mr Jobson's report to councillors disclosed that 20 primary schools recorded no incidents of either bullying or racism over the two-year period. In the previous three years, more than 30 primary schools made nil returns.
It states: "Information from individual schools indicates that this significant decrease is due to improved reporting systems rather than a decrease in incidents."
No secondary schools made nil returns for the period covering 2002-2004, although four had done so for the previous session.
Overall, Edinburgh primary schools reported 375 bullying and 225 racist incidents in 1999-2000, a total of 600. In 2003-04, the figures, respectively, were 252 and 173, making a total of 425.
Officials will now investigate whether under-reporting is responsible for this drop.
In the secondary sector in 1999-2000, there were 298 bullying and 45 racist incidents, a total of 343. This compares to the 2003-04 picture of 285 bullying and 64 racist cases reported, a total of 349.
Andrew Mellor, manager of the Anti-Bullying Network based at Edinburgh University, said that currently only three local authorities published figures on bullying and Edinburgh was the only council to do so for bullying and racism.
"I don't think any conclusions can be drawn from figures like this on how successful or unsuccessful schools are in tackling bullying," Mr Mellor said. "The only inference that can be drawn is about how good schools are at recording incidents - which is a totally different thing."
He, too, queried whether schools should be reporting nil returns, saying:
"Bullying happens in every school that I know of in the world. From the state of knowledge we have at the moment, bullying is impossible to eradicate.
"The most optimistic research from Scandinavia suggests that the best we can hope for is a reduction of 50 per cent, although that has never been replicated elsewhere. A more realistic reduction might be 20 per cent."