In this paper we investigate the construction of efficient secret sharing schemes by using a technique called hypergraph decomposition, extending in a non-trivial way the previously studied graph decomposition technique. A major advantage advantage of hypergraph decomposition is that it applies to any access structure, rather than only structures representable as graphs. As a consequence we obtain secret sharing schemes for several classes of access structures with improved efficiency over previous results. We also obtain an elementary characterization of the ideal access structures among the hyperstars, which is of independent interest.