  In this paper, we consider the elliptic relative equilibria of four-body
problem with two infinitesimal masses. The most interesting case is when the
two small masses tend to the same Lagrangian point $L_4$ (or $L_5$). In
\cite{Xia}, Z. Xia showed that there exist four central configurations: two of
them are non-convex, and the other two are convex. We prove that the elliptic
relative equilibria raised from the non-convex central configurations are
always linearly unstable; while for the elliptic relative equilibria raised
from the convex central configurations, the conditions of linear stability with
respect to the parameters are given.
