Substantial improvements in the computational effort in a density matrix re
normalisation program can be made by utilising symmetries of the Hamiltonia
n. Extra quantum numbers are always desirable to include in the calculation
, since it allows the Hilbert space of the superblock to be refined. Since
the speed of the calculation is approximately O(n(3)) in superblock states,
the speed increase in targeting a specific total spin state can be conside
rable. In this paper a new density matrix renormalisation algorithm is pres
ented which conserves the total spin. The general procedure obtained works
fbr any operator, even operators that do not commute with the Hamiltonian.