The aim of this paper is to derive a new robust stability margin. Known sufficient conditions for robust stability stated in gap-metric sense contain inherent conservativeness in the formulation of the various steps. In this paper conservativeness in one of the steps is removed, resulting in a new robustness margin. The key issue is that more information of the specific controller is taken into consideration. The resulting robustness margin is less conservative than the margin in directed gap-metric sense and is as easy to compute. The advantage of this robustness margin will be illustrated by an example.