However, the other measure of unemployment, the Labour Force Survey, rose by 0.1 percentage points to 6.2%.
That is higher than the UK unemployment rate which was unchanged at 5.5%.
The figures also show long-term unemployment in Northern Ireland is significantly above the UK rate.
Other figures show that output in Northern Ireland's service sector, the largest segment of the economy, grew slightly in the second quarter of the year.
Output was 0.5% higher compared to the first quarter of the year and 0.7% higher than the same point in 2014.
The strongest growth was in the retailing and hospitality sectors which was up 2.2% compared to the second quarter of 2014.
Analysis: BBC News NI Economics and Business Editor John Campbell
Northern Ireland's recovery has been weaker than in the UK as a whole and these figures suggest an economy which is just about growing.
The labour market picture is more complicated than just a falling claimant count - for example long-term unemployment is a real problem.
One of the more concerning factors is a slowdown in some parts of the manufacturing sector.
It has been a star performer in the last couple of years, but external factors like the strength of sterling appear to be taking a toll.
The picture was mixed in the production sector, which includes manufacturing.
Output was up by 1% over the year, but down by 1.9% compared to the first quarter of the year.
The food and drink sector is under particular pressure - output is almost 5% down compared to the second quarter of 2014.
That is likely to be related to global falls in commodity prices, particularly in the dairy sector.
The number of people claiming unemployment benefits in Northern Ireland fell by 1,000 in August to 42,000.