The number of people on the Live Register fell this month, according to the latest figures from the Central Statistics Office.
The seasonally adjusted figure dropped by 5,400 from August, to 449,600, the first fall since February.
This figure is more closely watched as it strips out seasonal changes, such as the return of students to college.
The headline figure fell by 24,506 to 442,417.
The CSO said the unemployment rate fell back to 13.7% in September from 13.8% in August. Men accounted for 2,600 of the seasonally adjusted fall, with women accounting for 2,900.
The CSO also said that there were 39,960 new claimants on the Live Register in September, up from just over 36,000 in August.
This figure is not the same as the monthly change in the Live Register, which is affected by people closing claims and moving between different schemes.
The number of people signing on for more than a year fell back slightly in September, though long-term claimants still make up a third of the total number of people on the Live Register.
A breakdown by occupation showed that the biggest increase in the numbers signing on in the last six months has been in the professional category, with an increase of 12.2%.
The Live Register includes some part-time, seasonal and casual workers. It is not designed to measure unemployment, though it is regarded as the most up-to-date indicator of the state of the jobs market.
Social Protection Minister Éamon Ó Cuív welcomed the figures, which he said represented the biggest ever monthly fall in unemployment.
He predicted that the jobless trend would level off by the end of the year but would still be unacceptably high.
The Irish National Organisation for the Unemployed has said the reduction in the number of people on the Live Register does not mean more people have gone into employment.
The organisation has said the reasons for the reduction need to be analysed and dealt with.
John Stewart of the INOU said emigration and the technicalities with social welfare payments are factors in removing people from the Live Register.
Chambers Ireland Deputy Chief Executive Seán Murphy said: 'While 5,400 fewer people are now signing on is positive, this may be linked to parents returning to work after the school holidays, students going back to college and people emigrating.
'We cannot assume that such a decline will continue every month.'
Fine Gael's Richard Bruton said the latest figures show the effects of the rise in emigration.
Mr Bruton said: 'Sadly, this small let-up in the relentless rise in unemployment does not reflect any recovery in employment levels in the economy.
'This was confirmed by the CSO's national household survey last week which again showed falling employment levels. Instead, it reflects the scourge of rising emigration.'
