* C$ at C$1.0395 to US$, or 96.20 U.S. cents * U.S. housing and consumer confidence data helps greenback * Bank of Canada's Wednesday rate decision statement eyed * Prices of government bonds fall across the curve By Alastair Sharp TORONTO, May 28 (Reuters) - The Canadian dollar weakened by more than half a cent against its U.S. counterpart on Tuesday, as the greenback gained on robust economic data that supported a view of the Federal Reserve starting to unwind its stimulus program in coming months. The loonie, as Canada's currency is colloquially known, has fallen sharply in recent weeks as domestic data suggests the economy will lag behind its larger neighbor, the United States. It was not alone on Tuesday, as a string of major currencies including the euro and yen slipped against the U.S. dollar while North American stock markets gained. "We have had strong equities but a generally weak environment for (non-U.S.) currencies today," said Camilla Sutton, chief currency strategist at Scotiabank. Currency traders are also looking ahead to the Bank of Canada rate decision on Wednesday, as they consider the outside chance that outgoing Governor Mark Carney moves the central bank to a neutral stance. "We expect either a similar statement, or slightly less hawkish ... so the surprise would be if it is substantially more dovish," Sutton said. She said the broad move in currencies was largely a reaction to several pieces of U.S. data that supported the notion that the Fed's monetary easing could soon be slowed. The S&P/Case Shiller index showed that U.S. home prices accelerated by the most in nearly seven years in March, while separate data showing surging consumer confidence pointed to some resilience for the economic recovery. The Canadian dollar ended the session trading at C$1.0395 to the greenback, or 96.20 U.S. cents, compared with C$1.0337, or 96.74 U.S. cents, at Monday's North American close. "There definitely seems to be a desire to take some exposure to Canada off the table at the moment," said Shaun Osborne, chief currency strategist at TD Securities. Earlier in May, the loonie had almost breached equal value with the greenback, while several months ago it was worth more than the U.S. dollar as it appeared that the Bank of Canada was much more likely to hike rates before the U.S. Federal Reserve would do so. A Reuters poll shows economists don't expect any tightening in Canada until the end of next year as domestic data keeps showing weakness. Some economists have questioned whether the central bank might drop a key phrase about plans to raise borrowing costs eventually. That language makes Canada's central bank the only one among the Group of Seven with an explicit tightening bias. But others have suggested that Carney is unlikely to make a policy shift with the last rate announcement before he leaves to head the Bank of England in July. "There is a train of thought in the market that on the basis of the data in Canada there is a justification perhaps for the bank moving to a neutral stance," Osborne said, adding that a change in policy is not his base assumption. He said the loonie could test C$1.06 within weeks, and that dropping the tightening bias would likely push the currency through C$1.04 on Wednesday. The price of Canadian government debt fell across the curve, with the longer end plummeting. The two-year bond lost 6 Canadian cents to yield 1.073 percent, while the benchmark 10-year bond sank 90 Canadian cents to yield 2.084 percent. The rise in Canadian yields was less than that seen south of the border, where the Fed's eventual pulling back on bond purchases would have a more direct impact.