* Service sector fall slowest since September 2008
* Business sentiment reaches 40-month high
* Job cuts pick up again, but remain modest
By Daniel Flynn
ROME, Oct 5 (Reuters) - Italy's service sector shrank at the slowest rate in a year in September thanks partly to an improvement in business sentiment, but new orders continued to contract and job losses accelerated, data showed on Monday.
The Markit/ADACI Purchasing Managers' Index, which covers companies from hotels to insurance brokers that make up two-thirds of the euro zone's No. 3 economy, rose to 48.5 from 46.4 the previous month.
That was the highest reading since the collapse of Lehman Brothers in September 2008 triggered a collapse of confidence in the global financial sector. The index has languished below the 50 mark separating growth from contraction since November 2007.
The figure was at the top of the range of a Reuters survey of 8 analysts, which gave a median forecast of 47.4.
In a tentative sign that demand for services was stabilising, new business fell at its slowest rate in a year, with the sub-index rising to 48.0 from 45.1 in August. Italy's 1.5 trillion euro economy entered recession in spring 2008.
Business sentiment rose to a 40-month high, with 58 percent of panellists reporting positive expectations for future business activity thanks to a improving economic outlook.
Optimism was strongest in the financial intermediation sector, followed by post and telecoms.
"Service providers are confident that the economy will emerge from recession within the next twelve months, with business expectations rising to a forty-month high," said Andrew Self, economist at Markit, who nonetheless urged caution.
"Job losses in the dominant service sector accelerated during September, raising the possibility that unstable labour market conditions will dampen any rise in consumer spending, a key factor in pulling any economy out of recession."
After a slowdown in August, the rate of job cuts picked up again last month but remained relatively modest. Only 12 percent of firms cut staff, while 7 percent hired new workers.
On a positive note, PMI data from the retail sector pointed to the weakest reduction in sales since October 2007 in September, Self said.
Input prices remained broadly flat in September, while output prices fell sharply, reflecting stiff competition in all sectors especially post and telecoms and hotels and restaurants.
The improvement in the services index reflected a rise in September's PMI manufacturing survey published on Thursday to 47.6, showing both pillars of Italy's economy approaching the crucial inflection point of 50.
Most economists predict Italy's economy will exit its worst post-war recession in the third or probably fourth quarter of this year, trailing larger euro zone economies France and Germany which posted growth in the second quarter.
Prime Minister Silvio Berlusconi's conservative government forecasts 0.7 percent growth in GDP next year, after a 4.8 percent contraction in 2009. (Editing by Andy Bruce)