  Motivated by Gilbarg-Weinberger's early work on asymptotic properties of
steady plane solutions of the Navier-Stokes equations on a neighborhood of
infinity \cite{GW1978} , we investigate asymptotic properties of steady plane
solutions of this system on a half-neighborhood of infinity with finite
Dirichlet integral and Navier-slip boundary condition, and obtain that the
velocity of the solution grows more slowly than $\sqrt{\log r}$, while the
pressure converges to $0$ along each ray passing through the origin.
