[en] A relativistic electron beam moving in a circular orbit in free space can radiate coherently if the wavelength of the synchrotron radiation exceeds the length of the bunch. In accelerators coherent radiation of the bunch is usually suppressed by the screening effect of the conducting walls of the vacuum chamber [1, 2]. The screening effect is weak for short wavelengths, but if the wavelength is shorter than the length of the bunch, the coherent radiation becomes exponentially small. However, if the beam density has initially a fluctuation with a characteristic length much shorter than the bunch length, this fluctuation will radiate coherently. If the radiation results in the growth of the initial fluctuation one can expect micro-bunching of the beam and an instability which leads to increased coherent radiation at short wavelengths. Experimentally self-excited coherent microwave radiation has been observed recently in NSLS VUV ring at BNL [3, 4], at the Synchrotron Ultraviolet Radiation Facility (SURF) at NIST [5], and at the Advanced Light Source at LBL [6]. A beam microwave instability induced by the coherent radiation of the density fluctuations is studied theoretically in this paper. We consider the case when CSR of a bunch as a whole is suppressed by screening and is caused by microstructures with longitudinal dimensions small compared to the bunch length. In this case, we can simplify consideration studying stability of a coasting beam with the line density equal to the local line density of the bunch