We generalize a sufficient condition for the stability of relative equilibr
ia in symmetric Hamiltonian systems, due to Patrick (1992 Relative equilibr
ia in Hamiltonian systems: the dynamic interpretation of nonlinear stabilit
y on a reduced phase space J. Gee. Phys. 9 111-19), to the case in which th
ese relative equilibria have non-trivial symmetry. We also describe a block
diagonalization that facilitates the use of this result in particular exam
ples and shows the relation between the stability of the relative equilibri
um and the Lyapunov stability of the associated singular reduced equilibriu
m.