One of the drawbacks of mainstream design methods is that their processes are based on crafty procedures rather than on rigorous mathematically founded procedures. Software designers spend a lot of time attempting to come up with an Architectural Design that is very often inefficient and not directly and systematically derived from the requirements. The lack of a systematic and a mathematical way to decompose the requirements into simpler pieces (components) leads to inconsistency of different parts of the designed system. This paper proposes a two stages Architectural Design as well as attempts to answer the following questions: (1) How can we derive the functional structure of the system (i.e., Functional Architectural Design) from its functional requirements? (2) What are the mathematical properties of an architectural component? (3) What kind of connectors might we have between these components? We adopt a state-oriented relational approach to the specification of the requirements and to the specification and the derivation of the Architectural Design.