  Using a recently developed perturbation formalism based on curvature
quantities, we complete our investigation of the linear stability of black
holes and solitons with Yang-Mills hair and a negative cosmological constant.
We show that those solutions which have no linear instabilities under odd- and
even-parity spherically symmetric perturbations remain stable under
even-parity, linear, non-spherically symmetric perturbations. Together with the
result from a previous work, we have therefore established the existence of
stable hairy black holes and solitons with anti-de Sitter asymptotic.
