Do timber buildings remove carbon from the atmosphere in the long run?

One of the advantages of timber buildings is regularly said to be their ability to effectively remove carbon from the atmosphere, through long term carbon storage.

Wouldn’t this require the timber used in the building to not decay, or at least to decay slower than the life cycle of a living tree?

But when the timber building decays it releases the carbon back into the atmosphere. Doesn’t this then close the circle, leading to a net effect of zero in the long run?