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There are numerous enterprise information system (EIS) engineering methodologies in the literature, each covering different aspects. However, in order to integrate them in an enterprise architecture, model-based engineering can be adopted. In such a case, a central system model is defined supporting all engineering activities. Zachman's matrix may be used as a basis for constructing such a model. Based on this assumption, we propose a systematic approach for the support of model-based EIS engineering process using Zachman matrix as EIS central model. Basic EIS engineering activities and the way they may be served by specific rows is explored, while the contribution of each system aspect (matrix column) is also taken into account. A conceptual model for model-based EIS engineering is also introduced. To explore the proposed concepts in practice, the system network cell is used as an example. Corresponding engineering tasks and sub-models are formed based on the proposed guidelines in a technology and methodology independent fashion. A case study based on the proposed concepts is also presented.