"Under neutral reciprocal sign epistasis, two genetic changes are jointly neutral, even though their individual effects are deleterious. By using the widely studied mapping from an RNA sequence to secondary structure, we investigate the effect of this kind of epistasis on neutral spaces corresponding to networks of genotypes that fold to the same secondary structure. Neutral networks for RNA structures with n bonds are typically fragmented into at least 2^n different neutral components that cannot be connected by single point mutations. By exhaustive enumeration of all RNA secondary structures of sequences of length 15 we show that most networks are not dominated by one neutral component, but are rather broken up into multiple large components. Although they generate the same phenotype, components of a single neutral network are heterogeneous, showing wide variations in their robustness and their evolvability. Both properties are correlated with component size, rather than with the size of their underlying neutral network. In particular, sets of accessible phenotypes can vary quite strongly between components. Thus, the potential for future innovation is contingent on which neutral component a population occupies. We further argue that neutral reciprocal sign epistasis may have similar consequences for neutral evolution of other biological systems as well."