  In \cite{LZ4}, the authors proved that as long as the one-directional
derivative of the initial velocity is sufficiently small in some scaling
invariant spaces, then the classical Navier-Stokes system has a global unique
solution. The goal of this paper is to extend this type of result to the 3-D
anisotropic Navier-Stokes system $(ANS)$ with only horizontal dissipation. More
precisely, given initial data $u_0=(u_0^\h,u_0^3)\in \cB^{0,\f12},$ $(ANS)$ has
a unique global solution provided that $|D_\h|^{-1}\pa_3u_0$ is sufficiently
small in the scaling invariant space $\cB^{0,\f12}.$
