  Muon-spin relaxation results on the pyrochlore iridate Nd$_2$Ir$_2$O$_7$ are
reported. Spontaneous coherent muon-spin precession below the metal-insulator
transition (MIT) temperature of about 33 K is observed, indicating the
appearance of a long-ranged magnetic ordering of Ir$^{4+}$ moments. With
further decrease in temperature, the internal field at the muon site increases
again below about 9 K. The second increase of internal field suggests the
ordering of Nd$^{3+}$ moments, which is consistent with a previous neutron
experiment. Our results suggest that the MIT and magnetic ordering of Ir$^{4+}$
moments have a close relationship and that the large spin-orbit coupling of Ir
5\textit{d} electrons plays a key role for both MIT and the mechanism of the
magnetic ordering in pyrochlore iridates in the insulting ground state.
