Summary: The stability is an expected property for refinable vectors, which is widely considered in the study of refinement equations. There are two types of stability for refinable vectors. One is the ordinary-stability, the other is the vector-stability. The ordinary-stability considers the stability of entries of refinable vectors, but the vector-stability considers the stability of refinable vectors themselves where they are considered as elements of super Hilbert spaces. In this paper, we give a necessary and sufficient condition for refinable vectors to be vector-stable. Our results improve some known ones.