  Let $A$ be a representation-finite self-injective algebra over an
algebraically closed field $k$. We give a new characterization for an
orthogonal system in the stable module category $A$-$\stmod$ to be a
simple-minded system. As a by-product, we show that every Nakayama-stable
orthogonal system in $A$-$\stmod$ extends to a simple-minded system.
