This is a bit of a trick question! All trees have timber, even if it's not a commercially valuable type of wood.

Here's why the question is tricky:

* "Timber" can mean different things: Sometimes it refers to specific types of wood used for construction, furniture, etc. Other times it just means the wood of a tree in general.

* Some trees have very soft or weak wood: These trees might not be suitable for building, but they still have wood. Examples include some willows, poplars, and palm trees.

So, the answer is that there is no tree with absolutely NO timber. All trees have wood.