Diocotron instability has been observed in the pure electron plasma formed in a split cathode coaxial diode. This plasma consists of electrons, trapped in the longitudinal potential well between the two parts of the cathode. The mathematical model of the electron squeezed state, which allows the calculation of the equilibrium plasma density, is presented. The model is applied in a comprehensive analysis of experimental data, and the presence of the diocotron instability is unambiguously confirmed.