* Canadian dollar strengthens 0.3% against the greenback

* Touches its strongest since Aug. 4 at 1.3337

* Canada's annual inflation rate holds steady at 3.1%

* Canada-U.S. 2-year spread narrows by 2.6 basis points

TORONTO, Dec 19 (Reuters) - The Canadian dollar strengthened to a four-and-a-half-month high against its U.S. counterpart on Tuesday as investors reduced bets on an early start to Bank of Canada interest rate cuts after domestic data showed inflation holding steady in November.

The loonie was trading 0.3% higher at 1.3355 to the greenback, or 74.88 U.S. cents, after touching its strongest intraday level since Aug. 4 at 1.3337.

Canada's annual inflation rate was 3.1% in November, matching October's pace, as slower growth in food prices and cheaper cellular services and fuel oil were offset by an acceleration in prices of travel tours. Analysts had forecast inflation to ease to 2.9%.

"Today's print just shows that there's still that two-sided risk," said Michael Greenberg, SVP and portfolio manager, Franklin Templeton Investment Solutions. "Inflation is still a concern of course but the Bank also doesn't want to slow the economy too much and cause undue hardship on people."

Money markets see a roughly 40% chance the BoC will begin cutting interest rates in March, down from 50% before the data. The central bank's benchmark interest rate is at a 22-year high of 5%.

Adding to support for the loonie, the price of oil, one of Canada's major exports, was up 0.5% at $72.82 a barrel amid concerns about supply disruptions and the U.S. dollar lost ground against a basket of major currencies.

Canadian government bond yields were mixed across a flatter curve. The 2-year rose 2 basis points to 4.015%, while the gap between it and its U.S. equivalent narrowed by 2.6 basis points to 43.6 basis points in favor of the U.S. note. (Reporting by Fergal Smith)