  We predict a new candidate high-temperature high-pressure structure of
FeSiO$_3$ with space-group symmetry Cmmm by applying an evolutionary algorithm
within DFT+U that we call post-perovskite II (PPv-II). An exhaustive search
found no other competitive candidate structures with ABO$_3$ composition. We
compared the X-ray diffraction (XRD) pattern of FeSiO$_3$ PPv-II with
experimental results of the recently reported "H-phase" of (Fe,Mg)SiO$_3$. The
intensities and positions of two main X-ray diffraction peaks of PPv-II
FeSiO$_3$ compare well with those of the H-phase. We also calculated the static
equation of state, the enthalpy and the bulk modulus of the PPv-II phase and
compared it with those of perovskite (Pv) and post-perovskite (PPv) phases of
FeSiO$_3$. According to the static DFT+U computations the PPv-II phase of
FeSiO$_3$ is less stable than Pv and PPv phases under lower mantle pressure
conditions at T=0 K and has a higher volume. PPv-II may be entropically
stabilized, and may be a stable phase in Earth's lower mantle, coexisting with
{\alpha-PbO$_2$ (Columbite-structure) silica and perovskite, or with
magnesiowustite and/or ferropericlase, depending on bulk composition.
