  Using the stellar photometry catalogue based on the latest data release (DR4)
of the Sloan Digital Sky Survey (SDSS), a study of the Galactic structure using
star counts is carried out for selected areas of the sky. The sample areas are
selected along a circle at a Galactic latitude of +60$^\circ$, and 10 strips of
high Galactic latitude along different longitudes. Direct statistics of the
data show that the surface densities of $\ell$ from $180^{\circ}$ to
$360^{\circ}$ are systematically higher than those of $\ell$ from $0^{\circ}$
to $180^{\circ}$, defining a region of overdensity (in the direction of Virgo)
and another one of underdensity (in the direction of Ursa Major) with respect
to an axisymmetric model. It is shown by comparing the results from star counts
in the $(g-r)$ colour that the density deviations are due to an asymmetry of
the stellar density in the halo. Theoretical models for the surface density
profile are built and star counts are performed using a triaxial halo of which
the parameters are constrained by observational data. Two possible reasons for
the asymmetric structure are discussed.
