  Inspired by the superblock method of White, we introduce a simple
modification of the standard Renormalization Group (RG) technique for the study
of quantum lattice systems. Our method which takes into account the effect of
Boundary Conditions(BC), may be regarded as a simple way for obtaining first
estimates of many properties of quantum lattice systems. By applying this
method to the 1-dimensional free and interacting fermion system, we obtain the
ground state energy with much higher accuracy than the standard RG. We also
calculate the density-density correlation function in the free-fermion case
which shows good agreement with the exact result.
