  In the Bianchi I cosmology some subclasses of the Horndeski theory allow for
the non-standard anisotropy behavior. For example, the anisotropy is damped
near the initial singularity instead of tending to infinity. In this article,
we analyze the nonlinear anisotropic model with the linear potential.We have
considered an example of such theory, for which the anisotropy is always
finite. The anisotropy reaches its a maximum value at the initial moment. The
anisotropy suppression occurs during the inflationary stage, and it approaches
zero at later times. This cosmological model does not contain the singular
point.
