* PBOC lets midpoint contributors adjust "X" factor - sources
* Easing yuan depreciation pressure a trigger for the move-sources
* Move seen not an intent to drastically weaken the yuan (Adds detail, context, quotes)
BEIJING/SHANGHAI, Jan 9 (Reuters) - China's central bank has taken a step to loosen control over the yuan exchange rate, sources familiar with the matter told Reuters on Tuesday, reflecting confidence that depreciation pressures on the Chinese currency have eased for now.
The People's Bank of China (PBOC) effectively reduced the influence of the "counter-cyclical factor" it introduced in May last year to the formula it uses to determine the mid-point reference rate for the yuan's exchange rate against the U.S. dollar each day. That factor was designed to lessen the impact of market forces on the yuan's reference point.
Sources said the PBOC had notified banks that contribute mid-point estimates to it for the official rate calculation that they could adjust the counter-cyclical factor by themselves, effectively allowing them to minimise its influence on their exchange rate contributions.
One source said this reflected the fact that the yuan was no longer under depreciation pressure.
In response to Reuters' request for information about the matter, the PBOC said it was up to the contributing banks to determine the counter-cyclical factor coefficient independently.
The formula the PBOC uses to determine the next day's midpoint fixing factors in the yuan settlement rate against the U.S. dollar at 4:30 p.m. (0830 GMT), along with changes in the trade-weighted basket of currencies and the counter-cyclical factor.
When it introduced that "X" factor, the PBOC said it would help to better reflect supply and demand, lessen possible "herd effects" in the market and guide the market to focus more on macroeconomic fundamentals.
But many traders saw it as a tool to reduce price swings and counteract pressure on the yuan after a rough 2016 when the Chinese currency lost about 6.5 percent against the dollar.
The yuan slipped after the news, finishing onshore trade at 6.5207 per dollar at 0830 GMT, weakening 0.34 percent from the previous late night close.
The offshore yuan was trading weaker at 6.5326 per dollar at 1056 GMT.
The yuan is allowed to trade within a band of two percent on either side of the daily midpoint.
The change could trigger further yuan weakening, said one currency trader at a foreign bank in Shanghai who forecast that it could test the 6.6 yuan, or renminbi, per dollar level.
Stephen Gallo, European head of FX Strategy at Bank of Montreal, said in a note he thinks this "doesn't drastically shift the balance of forces" in the yuan-dollar exchange rate.
"If market forces will now be allowed to play a greater role in the level of the dollar-yuan mid-rate, the general downward trend in the U.S. dollar can presumably be transmitted through USDRMB more easily. Therefore, today's move doesn't signal an intent to drastically weaken the renminbi on the part of the PBOC," he wrote.
Analysts at Nomura also agreed it did not mean China wanted to allow the yuan to depreciate.
"We do not believe this is the goal and see the change as likely related to authorities allowing for greater FX flexibility," they said in a note.
"In our view, this means that, if CNY faces appreciation/depreciation pressures, it would likely translate into a greater move in the following day's fixing."
The yuan rose nearly 6.8 percent against the dollar in 2017, more than reversing the previous year's losses. Most of those gains were in the second half of the year after the introduction of the counter-cyclical factor as well as government efforts to plug outflows of capital and restore confidence in the yuan.
(Reporting by Beijing newsroom; Writing by John Ruwitch and Winni Zhou in Shanghai; Editing by Vidya Ranganathan and Jacqueline Wong)