  The orientation of a chiral magnetic domain wall in a racetrack determines
its dynamical properties. In equilibrium, magnetic domain walls are expected to
be oriented perpendicular to the stripe axis. We demonstrate the appearance of
a unidirectional domain wall tilt in out-of-plane magnetized stripes with
biaxial anisotropy and Dzyaloshinskii--Moriya interaction (DMI). The tilt is a
result of the interplay between the in-plane easy-axis anisotropy and DMI. We
show that the additional anisotropy and DMI prefer different domain wall
structure: anisotropy links the magnetization azimuthal angle inside the domain
wall with the anisotropy direction in contrast to DMI, which prefers the
magnetization perpendicular to the domain wall plane. Their balance with the
energy gain due to domain wall extension defines the equilibrium magnetization
the domain wall tilting. We demonstrate that the Walker field and the
corresponding Walker velocity of the domain wall can be enhanced in the system
supporting tilted walls.
