New figures from the Central Statistics Office show that the seasonally adjusted unemployment rate for August fell to 6.3% from 6.4% in July.
The jobless rate had stood at 7.9% the same time last year.
The decrease in unemployment in August reversed the rare rise seen in July.
The CSO said the seasonally adjusted number of people who were unemployed stood at 139,100 last month.
This was down from 140,800 in July and a decrease of 33,900 when compared to the same time last year.
Employment has grown strongly since the jobless rate peaked at 15.1% in 2012 when the country was in the middle of an international bailout.
Jobs growth expanded at its fastest rate since the financial crisis in the first quarter of the year.
The Finance Department has forecast that the unemployment rate will dip below 6% by the end of this year.
This means the economy could reach full employment next year with the rate forecast to remain at 5.5% from 2018 onwards.
The country's jobless rate compares with a current euro zone average of 9.1%.
Today's CSO figures also reveal that the seasonally adjusted unemployment rate in August was 7.1% for men, down from 9% the same time last year.
The seasonally adjusted unemployment rate for women was 5.2%, a decrease from the rate of 6.5% in August 2016.
But the seasonally adjusted unemployment rate for persons aged between 15 and 24 years stood at 12.7% in August, up from 12.3% in July.
Alan McQuaid, chief economist with Merrion, said the figures were a little better than expected and pointed to the unemployment rate here being significantly less than the euro zone average of 9.1%.
However, he expressed concern about the youth unemployment rate which rose to 12.7% in August from 12.3% in July.
"Youth unemployment remains too high, and while it has fallen from 17.8% at the beginning of 2016, it is worrying that the rate has started to increase again in the past three months," he said.
Alan McQuaid said although emigration had been a factor in keeping unemployment down since the financial crisis, the labour market has improved dramatically over the past few years, reflecting the strengthening of the economic recovery.
"The most recent migration estimates showed net inward migration of 3,100 in the year to April 2016 as against net outward migration of 11,600 in 2015, and the first positive figure since 2009."
Mariano Mamertino, EMEA economist with job search site, Indeed, said recent indications on post-Brexit relocations of financial services companies from London would likely drive further jobs growth.
However, he pointed out that some domestic constraints could act as a disincentive to workers coming here.
"The Irish labour market continues to be a magnet for European jobseekers. As the domestic labour market tightens, employers will increasingly look overseas to hire people with the appropriate skills, however the biggest challenge they will face is ensuring new potential new hires aren't put off by the lack of suitable rental accommodation in Dublin.
"According to the National Competitiveness Council’s rent affordability index of cities only Manchester, London and Amsterdam are less affordable than Dublin, and last month Daft.ie showed rents reaching an all-time high and supply of accommodation at an all-time low," he pointed out.