  We present a systematic analysis of perturbative Hexagonal(HG) mixing for
describing recent global fit neutrino mixing data with normal and inverted
hierarchy. The corrections to unperturbed mixing are parameterized in terms of
small orthogonal rotations (R) with modified PMNS matrix of the forms
\big($R_{\alpha\beta}^l\cdot V_{HG},~V_{HG}\cdot R_{\alpha\beta}^r,~V_{HG}\cdot
R_{\alpha\beta}^r \cdot R_{\gamma\delta}^r,~R_{\alpha\beta}^l \cdot
R_{\gamma\delta}^l \cdot V_{HG}$,~$R_{\alpha\beta}^l\cdot V_{HG}\cdot
R_{\gamma\delta}^r$\big ). Here $R_{\alpha\beta}^{l, r}$ is rotation in ij
sector and $V_{HG}$ is unperturbed Hexagonal mixing matrix. The detailed
numerical investigation of all possible cases is performed with scanning of
parameter space using $\chi^2$ approach. We found that the perturbative schemes
governed by single rotation are unable to fit the mixing angle data even at
$3\sigma$ level. The mixing schemes which involves two rotation matrices, only
\big($R_{12}^l \cdot R_{13}^l \cdot V_{HG}$, ~$R_{13}^l \cdot R_{12}^l \cdot
V_{HG}$,~$R_{13}^l \cdot V_{HG} \cdot R_{12}^r$,~$R_{12}^l \cdot V_{HG} \cdot
R_{12}^r$, ~$R_{13}^l \cdot V_{HG} \cdot R_{13}^r$\big ) are successful in
fitting all neutrino mixing angles within $1\sigma$ range for normal
hierarchy(NH). However for inverted hierarchy(IH), only $R_{13}^l \cdot V_{HG}
\cdot R_{13}^r$ is most preferable as it can fit all mixing angles at $1\sigma$
level. The remaining perturbative cases are either excluded at 3$\sigma$ level
or successful in producing mixing angles only at $2-3\sigma$ level. To study
the impact of phase parameter, we also looked into CP violating effects for
single rotation case. The predicted value of $\delta_{CP}$ lies in the range
$39.0^\circ(40.4^\circ) \le |\delta_{CP}| \le 78.7^\circ(79.2^\circ)$ for
$U_{12}^l\cdot V_{HM}$ and $U_{13}^l\cdot V_{HM}$ case with Normal(Inverted)
Hierarchy.
