  We investigate the renormalization group (RG) flow of SU(3) lattice gauge
theory in a two coupling space with couplings $\beta_{11}$ and $\beta_{12}$
corresponding to $1\times 1$ and $1\times 2$ loops respectively. Extensive
numerical calculations of the RG flow are made in the fourth quadrant of this
coupling space, i.e., $\beta_{11}>0$ and $\beta_{12}<0$. Swendsen's factor two
blocking and the Schwinger-Dyson method are used to find an effective action
for the blocked gauge field. The resulting renormalization group flow runs
quickly towards an attractive stream which has an approximate line shape. This
is numerical evidence of a renormalized trajectory which locates close to the
two coupling space. A model flow equation which incorporates a marginal
coupling (asymptotic scaling term), an irrelevant coupling and a
non-perturbative attraction towards the strong coupling limit reproduces
qualitatively the observed features. We further examine the scaling properties
of an action which is closer to the attractive stream than the currently used
improved actions. It is found that this action shows excellent restoration of
rotational symmetry even for coarse lattices with $a \sim 0.3$ fm.
