This paper presents a software component composition methodology based on Axiomatic Design theory and Design Structure Matrix. The methodology we propose helps overcome anomalies and functional problems such as deadlock. Our approach can be described in two steps. First, we decompose the system to detect coupled components by using the Design Structure Matrix. Secondly, we represent attribute and method dependencies of the coupled components to identify issues during software composition using Design Matrix (DM) of Axiomatic Design.