The cycle of spliceosome assembly, intron excision, and spliceosome disassembly involves large-scale structural rearrangements of U6 snRNA that are functionally important. U6 enters the splicing pathway bound to the Prp24 protein, which chaperones annealing of U6 to U4 RNA to form a U4/U6 di-snRNP. During catalytic activation of the assembled spliceosome, U4 snRNP is released and U6 is paired to U2 snRNA. Here we show that point mutations in U4 and U6 that decrease U4/U6 base-pairing in vivo are lethal in combination. However, this synthetic phenotype is rescued by a mutation in U6 that alters a U6-Prp24 contact and stabilizes U2/U6. Remarkably, the resulting viable triple mutant strain lacks detectable U4/U6 base-pairing and U4/U6 di-snRNP. Instead, this strain accumulates free U4 snRNP, protein-free U6 RNA, and a novel complex containing U2/U6 di-snRNP. Further mutational analysis indicates that disruption of the U6-Prp24 interaction rather than stabilization of U2/U6 renders stable U4/U6 di-snRNP assembly nonessential. We propose that an essential function of U4/U6 pairing is to displace Prp24 from U6 RNA, and thus a destabilized U6-Prp24 complex renders stable U4/U6 pairing nonessential.