* Canadian dollar at C$1.1138 or 89.78 U.S. cents * Bond prices higher across the maturity curve By Leah Schnurr TORONTO, Jan 31 (Reuters) - The Canadian dollar firmed against the greenback on Friday, bouncing back from a 4-1/2-year low in whip-saw trade, though the battered loonie was still set to end January with its biggest monthly loss in over two years. A shift by the Bank of Canada to a more dovish policy stance has weighed on the Canadian dollar in recent months and the pressure has intensified since the start of the year as investors have turned increasingly short against the currency. At the same time, risk aversion around the world has been heightened in the last week by a sell-off in emerging markets that investors are worried will spread. The Canadian dollar has hit new 4-1/2-year lows for four sessions in a row. The currency broke through the psychologically important C$1.12 area earlier in the day before reversing course. "It seems like before we're heading into the weekend, some people are position-squaring," said Rahim Madhavji, president at KnightsbridgeFX.com in Toronto. The Canadian dollar ended the North American session at C$1.1138 to the greenback, or 89.78 U.S. cents, firmer than Thursday's close of C$1.1166, or 89.56 U.S. cents. The loonie was set to end January down 4.5 percent against the greenback, its worst month since September 2011, according to Reuters data. "The downward trend in the Canadian dollar is too strong to fight or attempt to pick a bottom," Camilla Sutton, chief currency strategist at Scotiabank, wrote in a note. "We expect ongoing Canadian dollar weakness before it stabilizes in the second half of the year." The only domestic data for the day showed the Canadian economy grew by 0.2 percent in November, slightly softer than the month before, as a recovery in the oil industry overcame a decline in manufacturing. The figure matched economists' expectations. Investors were also watching developments on the proposed Keystone XL oil pipeline, which would carry crude from Canada's oil sands to the United States. A U.S. State Department study released on Friday said the pipeline is unlikely to increase the pace of oil sands development, raising pressure on U.S. President Barack Obama to approve the project. Approval for Keystone could provide support for the Canadian currency as it would point to increased jobs, growth and foreign investment for the country, said Madhavji. "All that comes down to our economy, which is good for the loonie." Canadian government bond prices were higher across the maturity curve, with the two-year up 4 Canadian cents to yield 0.950 percent and the benchmark 10-year up 26 Canadian cents to yield 2.342 percent.