  We investigate the existence of black hole solutions of four dimensional
$\mathfrak{su}(N)$ EYM theory with a negative cosmological constant. Our
analysis differs from previous works in that we generalise the field equations
to certain non-spherically symmetric spacetimes. We prove the existence of
non-trivial solutions for any integer $N$, with $N-1$ gauge degrees of freedom.
Specifically, we prove two results: existence of solutions for fixed values of
the initial parameters and as $|\Lambda|\rightarrow\infty$, and existence of
solutions for any $\Lambda<0$ in some neighbourhood of existing trivial
solutions. In both cases we can prove the existence of `nodeless' solutions,
i.e. such that all gauge field functions have no zeroes; this fact is of
interest as we anticipate that some of them may be stable.
