The paper describes an instability mechanism in a friction unit comprising a rotating flexible annular disk pressed to a rigid surface on the whole outer circumference. It is shown that for such a system, sliding friction forces set up a feedback between the orthogonal bending eigenmodes of the disk with the same form but different angular orientation. Due to axisymmetry, these modes have the same eigenfrequency. The feedback between the vibration modes with the same frequency leads to appearance of the circulation terms in the equations of motion and to instability. As a measure to suppress squeal, special apertures in the disk are suggested. The goal is to detach the paired eigenfrequencies to stabilize the system. The positioning of the apertures is discussed. The instability mechanism is investigated on the simple analytical model. More detailed finite-element analysis confirms the analytical prediction about the influence of the friction and axisymmetry on the instability and enables to prove the measures against friction induced vibrations.