  In applications of White's Density Matrix Renormalization Group (DMRG)
algorithm, computation time is dominated by the diagonalisation of large sparse
Hamiltonians by iterative diagonalisation algorithms, whose convergence can be
decisively accelerated by the usage of good start vectors. In this paper I show
how, using the Marshall sign rule, in a wide class of antiferromagnetic models
the number of diagonalization iterations can be reduced below 10, sometimes
down to 2, accelerating the DMRG by an order of magnitude. This acceleration,
applicable during the growth of long chains, complements the acceleration
procedure proposed by White. To illustrate the feasibility of the approach, I
show how it performs if applied to the calculation of the Haldane gap for S=2.
