  A new density matrix renormalisation group (DMRG) approach is presented for
quantum systems of two spatial dimensions. In particular, it is shown that it
is possible to create a multi-chain-type 2D DMRG approach which utilises
previously determined system and environment blocks {\it at all points}. One
firstly builds up effective quasi-1D system and environment blocks of width $L$
and these quasi-1D blocks are then used to as the initial building-blocks of a
new 2D infinite-lattice algorithm. This algorithm is found to be competitive
with those results of previous 2D DMRG algorithms and also of the best of other
approximate methods. An illustration of this is given for the spin-half and
spin-one Heisenberg models on the square lattice. The best results for the
ground-state energies per bond of the spin-half and spin-one square-lattice
Heisenberg antiferromagnets for the $N = 20 \times 20$ lattice using this
treatment are given by $E_g/N_B = -0.3321$ and $E_g/N_B = -1.1525$,
respectively.
