  The RNiO$_3$ perovskites are known to order antiferromagnetically below a
material-dependent N\'eel temperature $T_\text{N}$. We report experimental
evidence indicating the existence of a second magnetically-ordered phase in
TlNiO$_3$ above $T_\text{N} = 104$ K, obtained using nuclear magnetic resonance
and muon spin rotation spectroscopy. The new phase, which persists up to a
temperature $T_\text{N}^* = 202$ K, is suppressed by the application of an
external magnetic field of approximately 1 T. It is not yet known if such a
phase also exists in other perovskite nickelates.
