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UPDATE 1-China cbank buys net 4.5 bln yuan in FX in Jan, most since 2015

* C.bank FX purchases highest since Oct 2015

* Demand for FX falls amid yuan strength

(Adds milestone, yuan performance) BEIJING, Feb 14 (Reuters) - China's central bank purchased a net 4.5 billion yuan ($710.08 million) worth of foreign exchange in January, the most since October 2015, according to Reuters calculations based on central bank data released on Wednesday. Investors look to the data to estimate China's capital flows, with a net increase suggesting inflows and a decline pointing to outflows. The January net purchases compare with sales of 36.32 billion yuan in December and 208.8 billion yuan in the year-ago period. The People's Bank of China (PBOC) has made net purchases of foreign exchange in four of the last five months as the yuan appreciates and demand for foreign currencies among Chinese companies and individuals ebbs. The yuan ended January with a 3.5 percent gain against the dollar, its best monthly performance since market rates were unified in 1994, Thomson Reuters data showed, adding to a 6.8 percent rise last year. Data on Tuesday showed China's outbound investment rose nearly 40 percent in January amid signs authorities are less worried about capital flight.

($1 = 6.3373 Chinese yuan renminbi)

(Reporting by Beijing Monitoring Desk and Elias Glenn; Editing