  The low energy behaviour of the 2d antiferromagnetic Heisenberg model is
studied in the sector with total spins $S=0,1,2$ by means of a renormalization
group procedure, which generates a recursion formula for the interaction matrix
$\Delta_S^{(n+1)}$ of 4 neighbouring "$n$ clusters" of size $2^n\times 2^n$,
$n=1,2,3,...$ from the corresponding quantities $\Delta_S^{(n)}$. Conservation
of total spin $S$ is implemented explicitly and plays an important role. It is
shown, how the ground state energies $E_S^{(n+1)}$, $S=0,1,2$ approach each
other for increasing $n$, i.e. system size. The most relevant couplings in the
interaction matrices are generated by the transitions
$<S',m';n+1|S_q^*|S,m;n+1>$ between the ground states $|S,m;n+1>$
($m=-S,...,S$) on an $(n+1)$-cluster of size $2^{n+1}\times 2^{n+1}$, mediated
by the staggered spin operator $S_q^*$
