  The Density Matrix Renormalization Group (DMRG) is a state-of-the-art
numerical technique for a one dimensional quantum many-body system; but
calculating accurate results for a system with Periodic Boundary Condition
(PBC) from the conventional DMRG has been a challenging job from the inception
of DMRG. The recent development of the Matrix Product State (MPS) algorithm
gives a new approach to find accurate results for the one dimensional PBC
system. The most efficient implementation of the MPS algorithm can scale as
O($p \times m^3$), where $p$ can vary from 4 to $m^2$. In this paper, we
propose a new DMRG algorithm, which is very similar to the conventional DMRG
and gives comparable accuracy to that of MPS. The computation effort of the new
algorithm goes as O($m^3$) and the conventional DMRG code can be easily
modified for the new algorithm.
