(Reuters) - Stocks fell on Wednesday after a sharp rally in the previous session as investors set their sights again on Europe's debt problems.

U.S. investors began the new year pushing shares higher, with the broad S&P 500 index rising to its highest level since late October. The first trading day of the year often brings a lot of money into the markets.

Financial stocks were the top decliners in early trading after European banks dropped on concerns a tight credit market will make it expensive for them to raise capital and for euro-zone countries to refinance debt.

The S&P financial sector index lost 1 percent, the biggest loser among S&P sectors. Bank of America Corp was the top decliner on the Dow, falling 2.1 percent to $5.68.

Italy's biggest bank UniCredit sank nearly 10 percent after it launched a 7.5 billion euro ($9.8 billion) share offering at a 43 percent discount.

The offering "indicates the difficulty in raising capital under new requirements," and raises concerns of renewed contagion," said Bryan McCormick, an analyst at OptionMonster.com in Chicago.

The Dow Jones industrial average was down 28.04 points, or 0.23 percent, at 12,369.34. The Standard & Poor's 500 Index dipped 5.51 points, or 0.43 percent, at 1,271.55. The Nasdaq Composite Index took off 15.25 points, or 0.58 percent, at 2,633.47.

U.S. factory orders rose 1.8 percent in November, further evidence the economy is on the right track to recovery. But the data was not enough to offset the decline in the market.

In company news, AT&T Inc agreed to pay TiVo Inc a minimum of $215 million and additional monthly licensing fees to settle a patent infringement dispute. AT&T shares were up 0.8 percent at $30.64, while TiVo jumped 10.3 percent to $9.84.

(Reporting By Angela Moon; editing by Jeffrey Benkoe)

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