* Nikkei drops off 4-week high on profit-taking
* Cosmetic firms, other China-related shares hit hardest
* Limited reaction to Brexit saga
By Hideyuki Sano
TOKYO, Jan 16 (Reuters) - Japanese shares slid on Wednesday as investors took money off the table after a three-week rally, led by heavy losses for companies with exposure to China's economy a day after they enjoyed a boost from Chinese stimulus hopes.
Despite small gains on Wall Street the previous day, the Nikkei share average dropped 1 percent to 20,351, after briefly touching a four-week high of 20,580.
Its March 2018 low of 20,347 is seen as a major support level, a clear break of which could further sour the mood.
As with most equity markets, Japanese stocks shrugged off British Prime Minister Theresa May's crushing defeat on Tuesday of her Brexit deal in parliament.
Companies that are seen as dependent on Chinese demand met heavy selling, as investors tried to take advantage of their gains made the previous session after Beijing signalled more stimulus measures are in the cards.
Among them were cosmetic firms, with Shiseido tumbling 4.3 percent, more than offsetting Tuesday's 2.7 percent gains, to hit an 11-month low.
Rival Kose dropped 6.2 percent to its lowest levels since October 2017 despite a local media report that its April-Dec profits are seen hitting a record for that period.
Shippers dropped 2.2 percent while Murata Manufacturing, seen as a big supplier to Apple , dropped 2.7 percent, after a 5.3 percent jump the previous day.
Investors also took profits from other recent gainers. Hitachi fell 3.4 percent after a 16 percent surge in the previous two days, helped by a media report the firm is considering withdrawing from nuclear plant business.
"Today we are seeing a bit of profit-taking after the rally. Ultimately U.S.-China talks hold the key," said Soichiro Monji, senior economist at Daiwa SB Investments.
He noted the market was not helped by reported comments from United States Trade Representative Robert Lighthizer that he did not see any progress made on structural issues during U.S. talks with China last week.
"But in any diplomatic talks, negotiators will have to keep talking until the last minute as you don't want to be seen as having compromised easily. So we just have to wait until the end of February for the outcome," he said.
While global share markets rallied since late December on signs of easing Sino-U.S. trade tensions, investors have started to cool their enthusiasm for equities in the face of mounting evidence of slowing global growth, market players said.
The New York Federal Reserve's business activity index declined more than expected to its lowest level since May 2017 in another sign of troubles in the manufacturing sector.
The broader Topix fell 0.66 percent to 1,532. (Reporting by Hideyuki Sano Editing by Shri Navaratnam)