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The aim of this paper is to implement the wavelet preconditioner for the linear system corresponding to the discrete Poincaré-Steklov operator arising in the three fields formulation. In order to apply the preconditioner, we will introduce multiresolution analysis(MRA)for L 2 (0, 2) which is suitable in nonconforming domain decomposition. Extensive numerical results show that the condition number of the matrix after preconditioning is stabilized when the number of subdomains and elements per edge are large.Mathematics Subject Classification: 65N55, 65T60, 35J25.