SHANGHAI, Oct 20 (Reuters) - China"s yuan briefly rose to its highest point against the U.S. dollar in more than four-and-a-half months on Wednesday after the central bank set a much stronger daily fixing for the currency. But after touching a top of 6.3794 per dollar, its firmest since June 2, the yuan pulled back by midday on what traders said was corporate dollar demand following recent strong gains by the Chinese unit, while the dollar itself remained broadly steady. Traders said a 100 billion yuan ($15.65 billion) injection of cash into China"s financial system through the central bank"s daily open market operations had also helped to nudge the yuan lower. "Market sentiment was very unstable yesterday with heavy dollar selling and no clear sign of buying by big banks. But it still remains unclear how things will go from here," said a trader at a foreign bank. The yuan breached the key 6.4 per-dollar level on Tuesday to end its domestic trading session at a four-month high, lifted by market expectations that fallout from debt-laden developer China Evergrande Group can be contained and hopes that Sino-U.S. tensions were easing. On Wednesday, the People"s Bank of China set the yuan"s daily midpoint rate - which is informed by the previous day"s domestic close - at 6.4069 per dollar, its firmest since June 11. "The PBOC was largely calm (about) RMB appreciation and we expect the USD strength and rising global yields to drive the RMB back to the 6.4/6.5 range," Ken Cheung, chief Asian FX strategist at Mizuho Bank said in a note. The yuan"s rise has been broad, lifting it not just against the dollar but other currencies as well. On Wednesday, China"s trade-weighted CFETS yuan basket index rose to 100.29, its highest since Feb. 3, 2016, according to Reuters calculations. Spot yuan opened at 6.3898 per dollar and was changing hands at 6.3900 at midday, 79 pips weaker than Tuesday"s late session close. The offshore yuan retreated from Tuesday"s high point of 6.3685 to trade at 6.384 by midday. Analysts and traders widely expect the yuan to soften against the U.S. dollar as China"s slowing economy prompts monetary authorities to ease policy. On Wednesday, data showed that China"s new home prices stalled for the first time since February 2020 in September, hit by tightening credit due to an ongoing crackdown on speculative investment. The yuan market at 4:00AM GMT: ONSHORE SPOT: Item Current Previous Change PBOC midpoint 6.4069 6.4307 0.37% Spot yuan 6.39 6.3821 -0.12% Divergence from -0.26% midpoint* Spot change YTD 2.16% Spot change since 2005 29.52% revaluation Key indexes: Item Current Previous Change Thomson 100.6 100.39 0.2 Reuters/HKEX CNH index Dollar index 93.719 93.806 -0.1 *Divergence of the dollar/yuan exchange rate. Negative number indicates that spot yuan is trading stronger than the midpoint. The People"s Bank of China (PBOC) allows the exchange rate to rise or fall 2% from official midpoint rate it sets each morning. OFFSHORE CNH MARKET Instrument Current Difference from onshore Offshore spot yuan 6.384 0.09% * Offshore 6.572 -2.51% non-deliverable forwards ** *Premium for offshore spot over onshore **Figure reflects difference from PBOC"s official midpoint, since non-deliverable forwards are settled against the midpoint. . ($1 = 6.3908 Chinese yuan renminbi) (Reporting by Andrew Galbraith; Editing by Kim Coghill)