* Canadian dollar weakens 0.3% against the greenback * Loonie trades in a range of 1.2777 to 1.2824 * Price of U.S. oil rises 0.6% * Canadian bond yields rise across a steeper curve TORONTO, Feb 4 (Reuters) - The Canadian dollar weakened against its U.S. counterpart on Thursday as the greenback added to recent gains against a basket of major currencies and ahead of Canada"s monthly jobs report on Friday. The loonie was trading 0.3% lower at 1.2814 to the greenback, or 78.04 U.S. cents, having traded in a range of 1.2777 to 1.2824. The U.S. dollar strengthened to two-month highs as data pointed to an improvement in the U.S. economic outlook, bond yields rose and the price of oil, one of Canada"s major exports, hit a one-year high. U.S. crude prices were up 0.6% at $56.03 a barrel after the OPEC+ alliance of producers stuck to its reduced output policy and U.S. crude stocks fell, with optimism over a new U.S. pandemic relief bill adding further price support. Canada"s employment report for January is due on Friday, which could help guide Bank of Canada interest rate expectations. The central bank expects Canada"s economy to contract in the current quarter after lockdowns were introduced in a number of provinces to help contain the spread of the coronavirus pandemic. Ontario, Canada"s most populous province, said it will resume in-person classes for primary and secondary students across all regions by Feb. 16 following a recent drop in infections. Canadian government bond yields edged higher across a steeper curve, with the 10-year up nearly one basis point at 0.958%. It touched its highest intraday since March last year at 0.970%. (Reporting by Fergal Smith ; Editing by Kirsten Donovan)