The author presents an application of the Schur complement preconditioning method in order to eliminate the smallest eigenvalues of a symmetric matrix. Wavelets and their basic properties are described in order to motivate their application in this context, and wavelet-Galerkin discretization for the multiscale approach are presented. If the Schur complement with respect to a subspace containing the eigenvectors corresponding to the smallest eigenvalues is computed, then it is proved that these eigenvalues are eliminated in the Schur complement. The condition numbers of the preconditioned Schur complement are estimated and numerical investigations show the enormous reduction in the condition number.