The divide-and-conquer principle is a technique to obtain solutions for a large-scale problem by dividing it into smaller and manageable subproblems and by integrating these subsolutions. In engineering design, the principle is often used not just as a complexity management method but also as an embodiment method, although its formalization is unclear if not non-existing. This paper attempts to formalize the principle in the context of design of complex multi-disciplinary systems such as mechatronics systems. It proposes a theory of decomposition in conceptual design (system architecting), which extends the decomposition theory in traditional engineering design based on functional decomposition. The theory is applicable to system decomposition processes, in which building blocks necessary for decomposition are not available or must be newly designed during the processes. The theory uses parameter relations governed by physical phenomena realizing functions. A case study of system architecting of a printer is illustrated as a demonstration of the theory.