We theoretically predict instability of a zero-dc-current state of the two-dimensional electron system formed on the surface of liquid helium induced by the cyclotron resonance (CR). This conclusion follows from the theoretical analysis of the dc magnetoconductivity which takes into account the contribution from radiation in an exact way. A many-electron model of the dynamic structure factor of the 2D Coulomb liquid is used to describe the influence of strong internal forces acting between electrons. For low electron densities and high amplitudes of the microwave field, the dc magnetoconductivity is shown to become negative in the vicinity of the CR which causes the instability. This effect is strongly suppressed by Coulomb forces in the region of high densities.