  In 1993, the global stability of Minkowski spacetime has been proven in the
celebrated work of Christodoulou and Klainerman \cite{Ch-Kl}. In 2003,
Klainerman and Nicol\`o \cite{Kl-Ni} revisited Minkowski stability in the
exterior of an outgoing null cone. In \cite{Shen23}, the author extended the
results of \cite{Ch-Kl} to minimal decay assumptions. In this paper, we prove
that the exterior stability of Minkowski holds with decay which is borderline
compared to the minimal decay considered in \cite{Shen23}.
