The interconversion of ortho-hydrogen (oH(2)) and para-hydrogen (pH(2)), the two nuclear spin isomers of dihydrogen, requires a paramagnetic spin catalyst such as a nitroxide. We report the design and demonstration of spin catalysis of the interconversion of oH(2) and pH(2) incarcerated in an endofullerene based on a reversible nitroxide/hydroxylamine system. The system is an example of a reversible magnetic spin catalysis switch that can increase the rate of interconversion of the nuclear spin isomers of H(2) by a factor of -10(4).