Generally, the first step in modeling molecular magnets involves obtaining the low-lying eigenstates of a Heisenberg exchange Hamiltonian which conserves total spin and belongs usually to a non-Abelian point group. In quantum chemistry, it has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of the point group. Many attempts have been made over the years, but unfortunately these have not resulted in methods that are easy to implement, or even applicable to all point groups. Here we present a general technique which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin, which is applicable to all types of point groups and is easy to implement on a computer. We illustrate the power of the method by applying it to the molecular magnetic system, Cu6Fe8, with cubic symmetry. We emphasize that our method is applicable to spin clusters with arbitrary site spins and is easily extended to fermionic systems.