  It is well-known that the conjectured SL(2, Z) invariance of type IIB string
theory in ten dimensions also persists in lower dimensions when the theory is
compactified on tori. By making use of this recent observation, we construct an
infinite family of magnetically charged black hole solutions of type II
superstring theory in four space-time dimensions. These solutions are
characterized by two relatively prime integers corresponding to the magnetic
charges associated with the two gauge fields (from NS-NS and R-R sectors) of
the theory and form an SL(2, Z) multiplet. In the extremal limit these
solutions are stable as they are prevented from decaying into black holes of
lower masses by a `mass gap' equation.
