  The first hint of the neutrino mass hierarchy is believed to come from the
long-baseline experiment NO$\nu$A. Recent results from the NO$\nu$A shows a
mild preference towards the CP phase $\delta_{13} = -90^\circ$ and normal
hierarchy. Fortunately this is the favorable area of the parameter space which
does not suffer from the hierarchy-$\delta_{13}$ degeneracy and thus NO$\nu$A
can have good hierarchy sensitivity for this true combination of hierarchy and
$\delta_{13}$. Apart from the hierarchy-$\delta_{13}$ degeneracy there is also
the octant-$\delta_{13}$ degeneracy. But this does not affect the favorable
parameter space of NO$\nu$A as this degeneracy can be resolved with a balanced
neutrino and antineutrino run. However, ff we consider the existence of a light
sterile neutrino then there may be additional degeneracies which can spoil the
hierarchy sensitivity of NO$\nu$A even in the favorable parameter space. In the
present work we find that apart from the degeneracies mentioned above, there
are additional hierarchy and octant degeneracies that appear with the new phase
$\delta_{14}$ in the presence of a light sterile neutrino in the eV scale. In
contrast to the hierarchy and octant degeneracies appearing with $\delta_{13}$,
the parameter space for hierarchy-$\delta_{14}$ degeneracy is different in
neutrinos and antineutrinos though the octant-$\delta_{14}$ degeneracy behaves
similarly in neutrinos and antineutrinos. We study the effect of these
degeneracies on the hierarchy sensitivity of NO$\nu$A for the true normal
hierarchy.
