There isn't a metal that *doesn't burn* in the absolute sense. All metals, given the right conditions (high enough temperature and presence of an oxidizer), will react with oxygen and burn.

However, some metals are more resistant to burning than others. For example:

* Gold and Platinum are highly resistant to oxidation and are often used in jewelry and other applications where they need to withstand heat and exposure to air. They don't easily burn in typical conditions.

* Silver is also quite resistant to oxidation, but it can tarnish over time.

It's important to remember that even metals that are considered "noble" (like gold and platinum) can be burned under extreme conditions, like high temperatures or the presence of strong oxidizing agents.

So, the answer depends on what you mean by "burn."