  We consider the spacetimes corresponding to static Global Monopoles with
interior boundaries corresponding to a Black Hole Horizon and analyze the
behavior of the appropriate ADM mass as a function of the horizon radius r_H.
We find that for small enough r_H, this mass is negative as in the case of the
regular global monopoles, but that for large enough r_H the mass becomes
positive encountering an intermediate value for which we have a Black Hole with
zero ADM mass.
