The exosome plays key roles in RNA maturation and surveillance, but it is unclear how target RNAs are identified. We report the functional characterization of the yeast exosome component Rrp44, a member of the RNase II family. Recombinant Rrp44 and the purified TRAMP polyadenylation complex each specifically recognized tRNA(i)(Met) lacking a single m(1)A(58) modification, even in the presence of a large excess of total tRNA. This tRNA is otherwise mature and functional in translation in vivo but is presumably subtly misfolded. Complete degradation of the hyponnodified tRNA required both Rrp44 and the poly(A) polymerase activity of TRAMP. The intact exosome lacking only the catalytic activity of Rrp44 failed to degrade tRNAiMet, showing this to be a specific Rrp44 substrate. Recognition of hypomodified tRNA(i)(Met) by Rrp44 is genetically separable from its catalytic activity on other substrates, with the mutations mapping to distinct regions of the protein.