  We introduce a Quantum Monte Carlo (QMC) method which efficiently simulates
in a sign-problem-free way a broad class of frustrated $S=1/2$ models with
competing antiferromagnetic interactions. Our scheme uses the basis of total
spin eigenstates of clusters of spins to avoid the severe sign problem faced by
other QMC methods. We also flag important limitations of the new method, and
comment on possibilities for further progress.
