* TSX falls 21.57 points, or 0.16 percent, to 13,298.30 * Eight of 10 main index sectors decline * National Bank climbs after results By John Tilak TORONTO, Dec 4 (Reuters) - Canada's main stock index slipped on Wednesday, hitting a five-week low, as improving economic data from the United States stirred worries that the U.S. Federal Reserve might soon begin rolling back its monetary stimulus program. Offsetting some of the weakness was a 1 percent gain in shares of National Bank of Canada, after the lender announced a 2-for-1 stock split and raised its dividend after reporting a 4 percent fall in fourth-quarter profit. Investors also eyed the Bank of Canada as it held its key interest rate steady but noted that the risks of undesirably weak inflation appeared greater than they did six weeks ago. Much of the focus remained on U.S. economic data, which has been increasingly upbeat. Reports showed U.S. private employers topped expectations in adding jobs in November and, separately, sales of new U.S. single-family homes recorded their biggest increase in nearly 33-1/2 years in October. "Investors should anticipate that the Fed is going to be relatively cautious about tapering," said Gavin Graham, chief strategy officer at Integris Pension Management Corp. "I don't think investors should be too concerned." The Toronto Stock Exchange's S&P/TSX composite index was down 21.57 points, or 0.16 percent, at 13,298.30, after touching 13,257.86, its lowest since Oct. 24. Graham said the Canadian benchmark - up about 7 percent this year - could record solid growth next year as sentiment for natural resource sectors improves. "It's fair to expect that we might seem some strength in the materials stocks and maybe a bit of a rebound in gold," said Graham, who expects the TSX to end 2014 at 14,500. Eight of the 10 main sectors on the index were in the red. Financials, the index's most heavily weighted sector, lost 0.4 percent. Royal Bank of Canada, the country's biggest lender, gave back 0.7 percent to C$69.09, and Toronto Dominion Bank declined 0.4 percent to C$95.74. But the materials group, which includes mining shares, was up 0.7 percent. Goldcorp Inc gained 1 percent to C$22.48, and Potash Corp climbed 0.5 percent to C$34. In other corporate news, Turquoise Hill Resources Ltd dropped 25 percent as shares began trading ex-rights. Shareholders are entitled to buy one share of Turquoise Hill at a discount for each share owned as of Dec. 6, but trades entered on Wednesday will not clear until after that record date.