A process for the production of melamine by pyrolysis of urea in a high-pressure reactor having a vertical central pipe is provided. The melamine flows upwards into the reactor from below, mixes in the lower part of the reactor with a urea melt, and optionally NH₃, introduced into the reactor from below, and emerges from the central pipe in the upper part of the central pipe. Part of the melamine formed flows downward in the annular space between the central pipe and reactor wall, and the remainder is expelled for further work-up. The off-gases are removed at the top of the reactor. A reactor for carrying out the process is also provided.