  A simple modification of the standard Renormalization Group (RG) technique
for the study of quantum spin systems is introduced. Our method which takes
into account the effect of boundary conditions by employing the concept of
superblock, may be regarded as a simple way for obtaining first estimates of
many properties of spin systems. By applying this method to the xxz spin 1/2
Heisenberg chain, we obtain the ground state energy with much higher accuracy
than the standard RG. We have also obtained the staggered magnetization and the
z-component of spin-spin correlation function which confirms the absence of
long-range order in the massless region of the 1D xxz model.
