We prove the instability of the gravitating regular sphaleron solution
s of the SU(2) Einstein-Yang-Mills-Higgs system with a Higgs doublet,
by studying the frequency spectrum of a class of radial perturbations.
With the help of a variational principle we show that there exist alw
ays unstable modes. Our method has the advantage that no detailed know
ledge of the equilibrium solution is required. It does, however, not d
irectly apply to black holes.