Summary: This paper introduces and presents theoretical analyses of constraint preconditioning via a Schilders-like factorization for nonsymmetric saddle-point problems. We extend Schilders’ factorization of a constraint preconditioner to a nonsymmetric matrix by using a different factorization. The eigenvalue and eigenvector distributions of the preconditioned matrix are determined. The choices of the parameter matrices in the extended Schilders factorization and the implementation of the preconditioning step are discussed. An upper bound on the degree of the minimum polynomial for the preconditioned matrix and the dimension of the corresponding Krylov subspace are determined, as well as the convergence behavior of a Krylov subspace method such as the generalized minimal residual method. Numerical experiments are presented.