All metal carbonates decompose upon heating, forming the corresponding metal oxide and carbon dioxide gas. The stability of the carbonate depends on the metal involved.

However, some metal carbonates are more stable than others. For instance, alkali metal carbonates (like sodium carbonate, Na2CO3) are relatively stable and decompose at higher temperatures compared to carbonates of less electropositive metals.

So, while no metal carbonate is completely "non-decomposable," some are more stable than others.