A new parametric mode in a Josephson tunnel junction biased in the zero-voltage mode is suggested. It is a nondegenerate parametric excitation where the junction plasma resonance represents the input circuit, and a junction geometrical resonance represents the idler circuit. This nondegenerate mode has been observed in analog experiments. In a real junction the realization of this mode of operation depends on the coupling between the plasma resonance and the geometrical resonance, and it is argued that without an external dc magnetic field the even geometrical resonances are most favorable for such a coupling. Journal of Applied Physics is copyrighted by The American Institute of Physics.