Eukaryal tRNA splicing endonucleases use the mature domains of pre-tRNAs as their primary recognition elements. However, they can also cleave in a mode that is independent of the mature domain, when substrates are able to form the bulge-helix-bulge structure (BHB), which is cleaved by archaeal tRNA endonucleases. We present evidence that the eukaryal enzymes cleave their substrates after forming a structure that resembles the BHB. Consequently, these enzymes can cleave substrates that lack the mature domain altogether. That raises the possibility that these enzymes could also cleave non-tRNA substrates that already have a BHB. As predicted, they can do so, both in vitro and in vivo.