Yuan touches new high but upward pressure cools

* Yuan hits record strong point before weakening

* Demand for yuan cooler than Friday, say traders

* C.bank sets strongest midpoint in five months

* Traders say cbank keen to slow yuan appreciation

(Updates to close)

SHANGHAI, Oct 29 (Reuters) - The yuan hit another record high on Monday, but then slipped back as traders said pressure on the Chinese currency eased from levels seen late last week.

After touching 6.2371, the yuan closed at 6.2436 per dollar, up 0.08 percent on Friday's close of 6.2489.

Traders said the fervour for the currency seen last Thursday and Friday -- when it hit the strong-side limit for the first time and stayed there for sustained periods -- seemed to have declined.

``Everyone has cooled off a little,'' said a trader at a commercial bank in Shanghai after the morning session during which the new high was hit.

The yuan/dollar rate was unlikely to maintain the sustained pressure on the strong side trade band limit seen late last week, she added.

Though less marked than at the end of last week, yuan demand supported the currency, as traders continued to unwind dollar positions built up in the first half of 2012 when the greenback was rising.

``The market feeling is that yuan appreciation isn't over and that the trend has yet to turn,'' a trader at a joint-stock Shanghai bank said.

The People's Bank of China (PBOC) set its mid-point at 6.2992 per dollar. While that marked the strongest fix since May, it was only slightly stronger than Friday's fix of 6.3010.

At its strongest point on Monday, the yuan was 0.99 percent firmer than the fix, but it then weakened so the divergence was 0.88 percent at the close. The exchange rate can rise or fall 1 percent from the midpoint set by the central bank each day.

Traders said that it was fairly clear that the central bank had intervened on Friday, when the yuan weakened significantly just before the market close, after having hugged the strong-side limit all day.

Along with Monday's almost flat midpoint fix, Friday's action suggests that the central bank is keen to rein in the pace at which the yuan is allowed to appreciate.

The currency has now risen 2.5 percent since its weakest point of the year of 6.3967 on July 25, and 0.85 percent since the start of 2012.

(Reporting by Shanghai Newsroom; Editing by Richard Borsuk)