Summary: The regularization technique of a literature was further generalized to solve non-symmetric generalized saddle point problems. The unconditional convergence property of the corresponding iterative method and the spectral properties of the corresponding preconditioned matrix were proved. Based on the preconditioners, a relaxed preconditioning form was proposed and relevant conclusions about the eigenproperties of the preconditioned system were also obtained. The effectiveness of the proposed new preconditioners was illustrated by numerical experiments.