Stability of steady states of a planar geometry diode with counter flows of electrons and positrons is studied. The study is related to the elucidation of pulsar RF radiation nature. The equation for the electric field perturbation is derived. Its exact solution is obtained for the case of a homogeneous steady-state field. The study of the dispersion equation obtained has shown that there is a threshold for the inter-electrode gap value, above which steady-state solutions are unstable. The instability threshold turned out to be √2 times higher than the known Pierce threshold.