  We re-analyze the globally neutral non-Abelian black holes and present a
unified picture, classifying them into two types; Type I (black holes with
massless non-Abelian field) and Type II (black holes with ``massive"
non-Abelian field). For the Type II, there are two branches: The black hole in
the high-entropy branch is ``stable" and almost neutral, while that in the low
entropy branch, which is similar to the Type I, is unstable and locally
charged. To analyze their stabilities, we adopt the catastrophe theoretic
method, which reveals us a universal picture of stability of the black holes.
It is shown that the isolated Type II black hole has a fold catastrophe
structure.
  In a heat bath system, the Type I black hole shows a cusp catastrophe, while
the Type II has both fold and cusp catastrophe.
