A method for the production of melamine from urea via a high-pressure non-catalytic process in which molten urea is reacted to produce melamine, carbon dioxide, and ammonia, the by-product gases are separated from the melamine melt, and the melamine melt is treated with ammonia in a liquid-filled column to remove dissolved carbon dioxide, the treated melamine melt being solidified to produce high-purity melamine. In the liquid-filled column, or bubble column, the melamine melt is treated with between 0.02 and 3 tons of ammonia per ton of melamine, the bubble column being operated at a pressure of between 1 and 40 MPa and at a temperature between the melting point of melamine at prevailing pressure and 450.degree. C., with the residence time of the melamine melt in the bubble column being between 1 minute and 10 hours.