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We prove nonlinear stability for finite amplitude perturbations of planeCouette flow. A bound of the solution of the resolvent equation in the unstablecomplex half-plane is used to estimate the solution of the full nonlinearproblem.The result is a lower bound, including Reynolds number dependence,ofthe threshold amplitude below which all perturbations are stable. Our result isan improvement of the corresponding bound derived in \cite{KLH:1}.

Bounds for the Threshold Amplitude for Plane Couette Flow