An enzyme, purified 300-fold from Escherichia coli infected with bacteriophage T4, catalyzes the conversion of 5'-termini of polyribonucleotides to internal phosphodiester bonds. The reaction requires ATP and Mg(++). For every 5'-(32)P terminus rendered resistant to alkaline phosphatase, an equal amount of AMP and PPi are formed. Various polyribonucleotides are substrates in the reaction; to date, the best substrate is [5'-(32)P]polyriboadenylate. With the latter substrate, no evidence of intermolecular reaction was obtained. However, the 5'-(32)P termini of poly(A) rendered resistant to alkaline phosphatase are also resistant to attack by RNase II, polynucleotide phosphorylase, and low concentrations of venom phosphodiesterase. Since the product formed with poly(A) lacks 3'-hydroxyl ends, as measured with these exonucleases, the enzyme appears to convert linear molecules of polyriboadenylate to a circular form by the intramolecular covalent linkage of the 5'-phosphate end to the 3'-hydroxyl terminus.