The essential splicing factor Prp24 contains four RNA Recognition Motif (RRM) domains, and functions to anneal U6 and U4 RNAs during spliceosome assembly. Here, we report the structure and characterization of the C-terminal RRM4. This domain adopts a novel non-canonical RRM fold with two additional flanking α-helices that occlude its β-sheet face, forming an occluded RRM (oRRM) domain. The flanking helices form a large electropositive surface. oRRM4 binds to and unwinds the U6 internal stem loop (U6 ISL), a stable helix that must be unwound during U4/U6 assembly. NMR data indicate that the process starts with the terminal base pairs of the helix and proceeds toward the loop. We propose a mechanistic and structural model of Prp24's annealing activity in which oRRM4 functions to destabilize the U6 ISL during U4/U6 assembly.