  Electronic nematic states with broken rotational symmetry often emerge in
correlated materials. In most iron-based superconductors, the nematic
anisotropy is oriented in the Fe-Fe direction of the iron square lattice.
Recently, a novel type of nematicity along the diagonal Fe-As direction has
been suggested in heavily hole-doped $A$Fe$_2$As$_2$ ($A=$ Rb or Cs). However,
the transport studies focusing on the fluctuations of such nematicity have
provided controversial results regarding the presence of diagonal nematic
order. Here we report high-resolution heat capacity measurements under in-plane
field rotation in RbFe$_2$As$_2$. While the temperature dependence of specific
heat shows no discernible anomaly associated with the nematic transition, the
field-angle dependence of specific heat near the superconducting transition (at
$\sim 2.8$ K) reveals clear two-fold oscillations within the plane, providing
thermodynamic evidence for the diagonal nematicity. Moreover, we find that
M\"ossbauer spectroscopy sensitively probes the nematic transition at $\sim 50$
K with no evidence of static magnetism. These results imply that the diagonal
nematicity in RbFe$_2$As$_2$ has a unique mechanism involving charge degrees of
freedom, having unusual thermodynamic properties of the transition.
