We propose a real-space renormalization group transformation for block
ing dynamically triangulated random surfaces. To verify that the RG tr
ansformation preserves the long distance physics of the surfaces we lo
ok at the string susceptibility exponent gamma(s) and the Hausdorff di
mension d(H) in the case of 2d pure gravity. To look for a fixed point
structure we study how several operators change under the RG transfor
mation.