* Canadian dollar weakens 0.1% against the greenback

* Trades in a range of 1.3591 to 1.3641

* Price of U.S. oil settles 0.8% higher

* Canadian yield curve inverts further

TORONTO, May 16 (Reuters) - The Canadian dollar edged lower against its U.S. counterpart on Thursday as the recent rally lost some momentum and investors assessed economic for signs the U.S. economy is slowing down.

The loonie was trading 0.1% lower at 1.3615 to the U.S. dollar, or 73.45 U.S. cents, after trading in a range of 1.3591 to 1.3641.

It follows six straight days of gains for the currency. On Wednesday, it touched a five-week high at 1.3589 as U.S. inflation data kept the door open to interest rate cuts this year.

"The CAD is digesting yesterday's gains against the USD -classic backing and filling before the next move," said Tony Valente, senior FX dealer at AscendantFX.

"Yesterday's U.S. inflation was on point and retail sales were very soft. This was followed by more soft U.S. data today reinforcing that an economic slowdown is emerging."

The number of Americans filing new claims for unemployment benefits fell last week, unwinding nearly half of the jump at the start of the month, indicating that labor market conditions remain fairly tight even as job growth is cooling.

"I would expect the USD to resume its fall against the CAD after this short respite," Valente said.

Canada's monthly inflation report, due next Tuesday, is seen as a major input into the Bank of Canada's decision in June whether to begin its own interest rate cutting campaign.

The price of oil, one of Canada's major exports, settled 0.8% higher at $79.23 a barrel, while Canadian government bond yields were mixed across a more deeply inverted curve.

The 2-year rose 4.4 basis points to 4.219%, while the 10-year was little changed at 3.574%. (Reporting by Fergal Smith; Editing by Daniel Wallis)