Many regulatory non-coding RNAs (ncRNAs) function through complementary binding with mRNAs or other ncRNAs, e.g., microRNAs, snoRNAs and bacterial sRNAs. Predicting these RNA interactions is essential for functional studies of putative ncRNAs or for the design of artificial RNAs. Many ncRNAs show clear signs of undergoing compensating base changes over evolutionary time. Here, we postulate that a non-negligible part of the existing RNA-RNA interactions contain preserved but covarying patterns of interactions. We present a novel method that takes compensating base changes across the binding sites into account. The algorithm works in two steps on two pre-generated multiple alignments. In the first step, individual base pairs with high reliability are found using the PETfold algorithm, which includes evolutionary and thermodynamic properties. In step two (where high reliability base pairs from step one are constrained as unpaired), the principle of cofolding is combined with hierarchical folding. The final prediction of intra- and inter-molecular base pairs consists of the reliabilities computed from the constrained expected accuracy scoring, which is an extended version of that used for individual multiple alignments. We derived a rather extensive algorithm. One of the advantages of our approach (in contrast to other RNA-RNA interaction prediction methods) is the application of covariance detection and prediction of pseudoknots between intra- and inter-molecular base pairs. As a proof of concept, we show an example and discuss the strengths and weaknesses of the approach.