The double‐stream cyclotron maser is a novel source of millimeter wavelength radiation in which two copropagating electron beams are caused to gyrate in a uniform axial magnetic field. The interaction of the slow cyclotron space‐charge wave on one beam with the fast cyclotron space‐charge wave on the other beam leads to high‐frequency bunching. The desired operating frequency is proportional to the electron cyclotron frequency (or a harmonic thereof) and inversely proportional to the difference in beam velocities, and can be achieved at low beam energies and axial magnetic fields. The linear instability growth rate is calculated from the fully relativistic Vlasov equation for the case of cold‐electron beams.