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Recently, a number of fast iteration methods for the solution of the structured linear system arising from the incompressible Navier-Stokes equations have been proposed by some authors. In order to evaluate the strong stability of these numerical algorithms, in this paper we deal with the structured backward error analysis for this type of structured linear system and present the explicit formula of the structured backward error. Based on the structured backward error, we perform some numerical experiments to compare the availability of some existing numerical algorithms.