The Preparata, Metze, and Chien ( \(\text {PMC}\) ) model and Maeng and Malek ( \(\text {M}{{\text {M}}^{\text {*}}}\) ) model are the two most widely adopted models in system−level fault diagnosis. Both of them assume that processors occur permanent failure and communication link never fail. Communication links may experience failures for various reasons. Therefore, the assumption that only processors occur failure is purely theoretical. Zhu et al. proposed a hybrid fault diagnosis model based on the \(\text {PMC}\) model, known as the \(\text {HPMC}\) (Hybrid Preparata, Metze, and Chien) model. In this paper, we propose a novel hybrid fault comparison diagnostic model, which is named the \(\textrm{HMM}^{*}\) (Hybrid Maeng and Malek) model. Under the \(\textrm{HMM}^{*}\) model, a test is composed of one node, its two adjacent nodes, and the associated edges. Additionally, we provide the sufficient and necessary conditions for the distinguishability of two hybrid consistent fault sets. Finally, as applications, the hybrid diagnosability of the \(n-\) \(\text {dimensional}\) hypercube under the \(\text {HM}{{\text {M}}^{\text {*}}}\) model is determined.