3'-5' RNA exonuclease that trims the 3' end of oligo(U) tracts of the pre-U6 small nuclear RNA (snRNA) molecule, leading to the formation of a mature U6 snRNA 3' end-terminated with a 2',3'-cyclic phosphate. Participates in the U6 snRNA 3' end processing that prevents U6 snRNA degradation. a 3'-end uridylyl-uridine-RNA = a 3'-end 2',3'-cyclophospho-uridine-RNA + uridine Belongs to the 2H phosphoesterase superfamily. USB1 family.