  We propose a two-level iterative scheme for solving general sparse linear
systems. The proposed scheme consists of a sparse preconditioner that increases
the skew-symmetric part and makes the main diagonal of the coefficient matrix
as close to the identity as possible. The preconditioned system is then solved
via a particular Minimal Residual Method for Shifted Skew-Symmetric Systems
(mrs). This leads to a two-level (inner and outer) iterative scheme where the
mrs has short term recurrences and satisfies an optimally condition. A
preconditioner for the inner system is designed via a skew-symmetry preserving
deflation strategy based on the skew-Lanczos process. We demonstrate the
robustness of the proposed scheme on sparse matrices from various applications.
