This paper presents an original methodology for Enterprise Architecture. Enterprise Architecture is the discipline whose purpose is to align more effectively the strategies of enterprises together with their processes and their resources (business and IT). Enterprise architecture is complex because it involves different types of practitioners with different goals and practices. Enterprise Architecture can be seen as an art; it is largely based on experience but does not have strong theoretical foundations. As a consequence, it is difficult to teach, to apply, and to support with computer-aided tools. This paper presents how system sciences, by defining the concept of the systemic paradigm, can provide these necessary theoretical foundations. Thanks to our systemic paradigm, the enterprise architects can improve their understanding of the existing methodologies and thus find explanations for the practical problems they encounter. This paper then gives a concrete example of the application of the systemic paradigm: the Systemic Enterprise Architecture Methodology (SEAM) - an original methodology. With SEAM, architects can use a methodology that alleviates most of their practical problems and that can be supported by a tool.