* Yuan hits new record strong point, near strong-side limit
* But yuan demand cooler than Friday say traders
* C.bank sets strongest midpoint in five months
* But midpoint virtually flat, as c.bank favors stability
SHANGHAI, Oct 29 (Reuters) - China's yuan hit a record high on Monday, creeping towards the strong-side limit of its daily trading band, but traders said upward pressure on the currency had eased from the last session.
The yuan strengthened to 6.2385 per dollar around midday, up 0.7 percent from Friday's close of 6.2489.
Despite the gains, traders said the fervour for the currency seen on Thursday and Friday last week -- when the currency hit the strong-side limit for the first time ever and stayed here for sustained periods -- seemed to have eased.
``I wouldn't be surprised if the rate hit the lower limit later today, but everyone has cooled off a little and I don't think it will stick to the limit like it did last Friday,'' said a trader at a commercial bank in Shanghai.
The People's Bank of China (PBOC) set its mid-point at 6.2992 per dollar. Though 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 morning, the currency hit 6.2371, 0.99 percent firmer than the fix. The exchange rate can rise or fall 1 percent from the midpoint set by the central bank each day.
Traders added 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 nearly flat midpoint fix, Friday's action suggests that the central bank is keen to rein in the rate at which the yuan is allowed to appreciate.
The currency has now risen 2.5 percent since hitting its weakest point of the year of 6.3967 on July 25, and 0.94 percent since the start of 2012.
(Reporting by Shanghai Newsroom; Editing by Kim Coghill)