RNA secondary structure plays an important role in the function of many RNAs, and structural features are often key to their interaction with other cellular components. Thus, there has been considerable interest in the prediction of secondary structures for RNA families. In this article, we present a new global structural alignment algorithm, RNAG, to predict consensus secondary structures for unaligned sequences. It uses a blocked Gibbs sampling algorithm, which has a theoretical advantage in convergence time. This algorithm iteratively samples from the conditional probability distributions P(Structure | Alignment) and P(Alignment | Structure). Not surprisingly, there is considerable uncertainly in the high-dimensional space of this difficult problem, which has so far received limited attention in this field. We show how the samples drawn from this algorithm can be used to more fully characterize the posterior space and to assess the uncertainty of predictions.