This paper provides a rigorous proof of the existence of an infinite number of black hole solutions to the Einstein-Yang/Mills equations with gauge group<i>SU</i>(2), for any event horizon. It is also demonstrated that the ADM mass of each solutions is finite, and that the corresponding Einstein metric tends to the associated Schwarzschild metric at a rate 1/<i>r</i> <sup>2</sup>, as<i>r</i> tends to infinity.