We propose a DNA-hairpin model for the processivity of telomeric-repeat addition. Concomitantly with template-RNA translocation after each repeat synthesis, the complementary DNA repeat, for example, AGGGTT, loops out in a noncanonical base-paired hairpin, thus freeing the RNA template for the next round of repeat synthesis. The DNA hairpin is temporarily stabilized by telomerase and the incoming dGTP but becomes realigned for processive telomere synthesis.