  Conventional studies of galaxy clustering within the framework of halo models
typically assume that the density profile of all dark matter haloes can be
approximated by the Navarro-Frenk-White (NFW) spherically symmetric profile.
However, both modern N-body simulations and observational data suggest that
most haloes are either oblate or prolate, and almost never spherical. In this
paper we present a modified model of the galaxy correlation function. In
addition to the five "classical" HOD parameters proposed by Zheng et al. 2007,
it includes an additional free parameter $\phi$ in the modified NFW density
profile describing the asymmetry of the host dark matter halo.
  Using a subhalo abundance matching model (SHAM), we populate galaxies within
BolshoiP N-body simulations. We compute the projected two-point correlation
function $w_p(r_p)$ for six stellar mass volume limited galaxy samples. We fit
our model to the results, and then compare the best-fit asymmetry parameter
$\phi$ (and other halo parameters) to the asymmetry of dark matter haloes
measured directly from the simulations and find that they agree within
1$\sigma$. We then fit our model to the $w_p(r_p)$ results from Zehavi et al.
2011 and compare halo parameters. We show that our model accurately retrieves
the halo asymmetry and other halo parameters. Additionally, we find $2-6\%$
differences between the halo masses ($\log M_{min}$ and $\log M_1$) estimated
by our model and "classical" HOD models. The model proposed in this paper can
serve as an alternative to multiparameter HOD models, since it can be used for
relatively small samples of galaxies.
