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 Labour-led authority said the proposals were part of a number of cuts aimed at combating a budget shortfall of £157m over the next four years.
A range of pupils, from pre-school age to young adults could be asked to pay up to £349 a year.
The move would save the authority £191,500.
Councillor Kevin Gillott, cabinet member for children and younger adults, said: "I know that at a time when families are struggling with rising costs and falling living standards people will be wondering why we are having to consider asking them to pay towards providing transport for their children.
"Sadly, we have no choice  as we're being forced by the government to make savings that mean the council will have to cut the amount of money it spends on providing services to Derbyshire families by a third."
The authority is also looking to reduce its housing-related support budget by £9m.
This would affect a range of groups, including people with learning disabilities and those at risk of domestic abuse.
The county council said it would begin its consultation on Monday.

The 28-year-old played 138 times for the club and represented Scotland Sevens between 2006 and 2014, including last year's Commonwealth Games.
"A difficult time has been made easier as it's not been a decision," said Grant.
"You just have to get on with it, accept things and move on."
Grant joined Edinburgh in 2009 after beginning his Scottish rugby career as an apprentice with Border Reivers.
A recipient of the John Macphail Scholarship in 2008, he broadened his experience playing with Auckland University in New Zealand, having played through Scotland's age grades, and went on to be part of the Scotland A team that secured a 35-0 victory over England Saxons in 2012.
"It's been a pretty emotional time, having to come to terms with the fact I have to stop playing due to injury but I have no regrets," added Grant.
"I'm really proud of what I've done, what I've achieved and what I've contributed."
Head coach Alan Solomons said: "Roddy's retirement is a sad day for both the club and Scottish rugby.
"I've been fortunate, over the years, to coach some terrific young men; Roddy is right up there with the best of the best. His contribution to the club has been immense, both on and off the field. He is a leader of men and the ultimate pro.
"He has the heart of a lion, an unbelievable work-rate and he knew our systems and his role within them to perfection. Roddy never had a bad game. He is certainly one of the most consistent players I have ever coached.
"We will miss him - he is one of a kind."
The number of people claiming unemployment benefits in Northern Ireland fell by 1,000 in August to 42,000.
[NEXT_CONCEPT]
School transport charges for students with special educational needs are being considered by Derbyshire County Council.
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Experienced Edinburgh flanker Roddy Grant has been forced to retire after failing to recover from a knee injury suffered at the end of last season.