* Canadian dollar strengthens 0.4% against greenback * Canadian payroll employment increases by 245,800 in March * Price of U.S. oil falls 0.2% * Canadian bond yields rise across a steeper curve TORONTO, May 27 (Reuters) - The Canadian dollar strengthened against its U.S. counterpart on Thursday, moving back in reach of a recent 6-year high as investors awaited U.S. inflation data on Friday that could provide clues on the Federal Reserve"s policy outlook. The loonie was trading 0.4% higher at 1.2069 to the greenback, or 82.86 U.S. cents. Last week, it touched its strongest level since May 2015 at 1.2013, bolstered by higher commodity prices and the Bank of Canada"s shift in April to a more hawkish stance. The central bank is likely to cut its bond-buying program again this year, possibly as soon as July, as provinces ease curbs to contain the coronavirus pandemic and inflation pressures build, analysts said. Economists expect data on Friday to show U.S. core PCE (personal consumption expenditures) prices jumping in April. Fed officials have downplayed concerns about inflation prompting a knee-jerk policy response but some have acknowledged that the time to talk about policy changes might be approaching. The price of oil, one of Canada"s major exports, was down 0.2% at $66.08 a barrel as concern about demand in India and the potential for a rise in Iranian supplies offset optimism over the U.S and European summer driving season. Canadian payroll employment increased by 245,800 in March, the strongest monthly growth since last September, Statistics Canada said. Tighter restrictions to curb the coronavirus pandemic are likely to have weighed on employment in April. Canadian government bond yields were higher across a steeper curve, tracking the move in U.S. Treasuries after data showed new orders for key U.S.-made capital goods increased more than expected in April. Canada"s 10-year bond yield rose 3.7 basis points to 1.487%, having rebounded from its lowest intraday level since mid-April on Wednesday at 1.444%. (Reporting by Fergal Smith; editing by Emelia Sithole-Matarise) Our Standards: The Thomson Reuters Trust Principles.