  We propose a parametrization for the growth index of the linear matter
perturbations, $\gamma(z)=\gamma_0+\frac{z}{1+z}\gamma_1$. The growth factor of
the perturbations parameterized as $\Omega_m^{\gamma}$ is analyzed for both the
$w$CDM model and the DGP model with our proposed form for $\gamma$. We find
that $\gamma_1$ is negative for the $w$CDM model but is positive for the DGP
model. Thus it provides another signature to discriminate them. We demonstrate
that $\Omega_m^{\gamma}$ with $\gamma$ taking our proposed form approximates
the growth factor very well both at low and high redshfits for both kinds of
models. In fact, the error is below 0.03% for the $\Lambda$CDM model and 0.18%
for the DGP model for all redshifts when $\Omega_{m0}=0.27$. Therefore, our
parametrization may be robustly used to constrain the growth index of different
models with the observational data which include points for redshifts ranging
from 0.15 to 3.8, thus providing discriminative signatures for different
models.
