  In the first part of the present work the $\mu-\tau $ symmetry of the
neutrino mass matrix is perturbed at its minimal level in order to produce
deviation from Tri-bimaximal mixing (TBM), which includes nonzero value of
reactor angle $\theta_{13}$ and maximal condition of $\tan^{2}\theta_{23}=1$.
The parametrisation of neutrino mass matrix which describes Normal hierarchy
(NH), has been addressed with minimum number of independent parameters, out of
which two parameters $\eta$ and $\alpha$ take care of $\theta_{12}$ and
$\theta_{13}$ respectively without any interference with mass eigenvalues. In
the second part the deviation from maximal condition $\tan^{2}\theta_{23}=1$,
along with the nonzero value of $\theta_{13}$, has been implemented with the
introduction of a perturbing matrix which breaks the $\mu-\tau $ symmetric mass
matrix. The model is found to be flexible enough to adjust itself with the
changing precise experimental results. The method is also applicable for
inverted hierarchy and quasi-degenerate cases.
