Safety arguments typically have some weaknesses. To show that the overall confidence in the safety argument is considered acceptable, it is necessary to identify the weaknesses associated with the aspects of a safety argument and supporting evidence, and manage them. Confidence arguments are built to show the existence of sufficient confidence in the developed safety arguments. In this paper, we propose an approach to systematically constructing confidence arguments and identifying the weaknesses of the software safety arguments. The proposed approach is described and illustrated with a running example.