A frequency-domain approach to derive stable reduced-order models for a stable linear discrete-invariant system is presented. The method is based on combining the Schwarz approximation with the bilinear transformation. An efficient algorithm that avoids the bilinear transformation is derived by which the bilinear Schwarz discrete models are derived directly in the z-domain. The state-space bilinear Schwarz approximation is also presented by which the lower-order time-domain model matrices are derived by suitable truncation of the original system matrices in the bilinear Schwarz canonical form. The aggregation matrix relating the original system and reduced model state vectors is also derived. A numerical example is included to illustrate the method.