Time-linearized computational fluid dynamic (CFD) models for the computation of unsteady flows in turbomachinery are now used routinely in the design and analysis of turbomachinery blade rows, particularly to predict the onset of flutter. A typical flutter analysis of a rotor requires one to compute unsteady flow solutions over the full range of interblade phase angles, and hence requires significant computational time even for relatively efficient time-linearized flow solvers. Typically, one might compute the unsteady aerodynamic damping at several dozen interblade phase angles to ensure that no single interblade phase angle will flutter. In this note, we describe a fast technique that significantly reduces the computational time required to perform such a flutter clearance analysis