  Continuing work initiated in an earlier publication [Yamada, Tsuchiya, and
Asada, Phys. Rev. D 91, 124016 (2015)], we reexamine the linear stability of
the triangular solution in the relativistic three-body problem for general
masses by the standard linear algebraic analysis. In this paper, we start with
the Einstein-Infeld-Hoffman form of equations of motion for $N$-body systems in
the uniformly rotating frame. As an extension of the previous work, we consider
general perturbations to the equilibrium, i.e. we take account of perturbations
orthogonal to the orbital plane, as well as perturbations lying on it. It is
found that the orthogonal perturbations depend on each other by the first
post-Newtonian (1PN) three-body interactions, though these are independent of
the lying ones likewise the Newtonian case. We also show that the orthogonal
perturbations do not affect the condition of stability. This is because these
always precess with two frequency modes; the same with the orbital frequency
and the slightly different one by the 1PN effect. The same condition of
stability with the previous one, which is valid even for the general
perturbations, is obtained from the lying perturbations.
