PIWI-interacting RNAs (piRNAs) protect the animal germ line by silencing transposons. Primary piRNAs, generated from transcripts of genomic transposon "junkyards" (piRNA clusters), are amplified by the "ping-pong" pathway, yielding secondary piRNAs. We report that secondary piRNAs, bound to the PIWI protein Ago3, can initiate primary piRNA production from cleaved transposon RNAs. The first ~26 nucleotides (nt) of each cleaved RNA becomes a secondary piRNA, but the subsequent ~26 nt become the first in a series of phased primary piRNAs that bind Piwi, allowing piRNAs to spread beyond the site of RNA cleavage. The ping-pong pathway increases only the abundance of piRNAs, whereas production of phased primary piRNAs from cleaved transposon RNAs adds sequence diversity to the piRNA pool, allowing adaptation to changes in transposon sequence.