  We investigate the renormalization group evolution of masses and mixing
angles of Majorana neutrinos under the `High Scale Mixing Unification'
hypothesis. Assuming the unification of quark-lepton mixing angles at a high
scale, we show that all the experimentally observed neutrino oscillation
parameters can be obtained, within 3-$\sigma$ range, through the running of
corresponding renormalization group equations provided neutrinos have same CP
parity and are quasi-degenerate. One of the novel results of our analysis is
that $\theta_{23}$ turns out to be non-maximal and lies in the second octant.
Furthermore, we derive new constraints on the allowed parameter space for the
unification scale, SUSY breaking scale and $\tan \beta$, for which the `High
Scale Mixing Unification' hypothesis works.
