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Yuan softens as c.bank signals desire for stability

* Yuan eases slightly to 6.2510/dollar

* Traders wary of hitting strong side of trading band

* Chinese currency still near all-time strong point

* Little impact from positive manufacturing PMI data

SHANGHAI, Oct 24 (Reuters) - China's yuan eased on Wednesday, responding to a slightly weaker central bank midpoint, but still hovered near recent record levels, as traders say corporate yuan demand remains robust.

The central bank set its midpoint at 6.3081 per dollar, barely weaker than Tuesday's fixing of 6.3078. It was the second straight session in which the midpoint was virtually flat, despite a rise in the dollar index overnight.

After setting a series of sharply stronger midpoints last week, traders say the flat fixings this week suggest the central bank may have limited appetite for further appreciation.

Corporate demand for yuan is still robust, but after the currency gained 0.1 percent on Tuesday, dealers adjusted their quotes weaker to limit the risk of hitting the strong-side limit of the yuan's allowable trading band.

The central bank allows the dollar/yuan rate to rise or fall by no more than 1 percent from the midpoint in a single day. At its midday level of 6.2510, spot yuan was within 0.1 percent of Tuesday's strong-side limit of 6.2450.

The yuan reached an all-time strong point of 6.2446 last Thursday and closed firmer than the psychologically important 6.25 level for the first time ever on Tuesday.

Traders and analysts are divided about whether central bank intervention is responsible for the yuan's recent rally, which has seen the currency strengthen by 2.3 percent since hitting its weakest point of the year at 6.3967 on July 25.

The slight weakening occurred despite a manufacturing survey released on Wednesday showing output at a three-month high in October. The China HSBC Flash Manufacturing Purchasing Managers Index (PMI) showed the manufacturing sector contracting for a 12th consecutive month, but at its slowest pace since July.

The onshore yuan rate rarely responds to macroeconomic indicators such as PMI, with traders typically focused on trade data, which more directly affects supply and demand for the yuan in the interbank market.

(Editing by Jacqueline Wong)