A mechanism of a squeaking noise due to a friction between a photoreceptor drum and a cleaning blade in a laser printer is presented in this paper. We have already revealed the oscillation is one of a coupled mode flutter via a friction. Then, we try to formulate a nonlinear amplitude equation of unstable vibration due to a coupled mode flutter as following steps. At first, we formulate a nonlinear equation of coupled vibration including the nonlinear component of an external force. Then, we reconstruct the nonlinear equation that consists of only unstable modes via an adjoint system. Secondly, we solve the nonlinear equation by the method of multiple scales, then, we reveal displacement of two modes when the self-excited vibration becomes steady state. Finally, we formulate an amplitude equation by combination of displacements of unstable mode and eigenfunctions given from eigenvalue analysis results, and then we inspect a validity of the led equation by comparing the calculation results of the experiment about some modified blades.