RNA polymerases (RNAPs) transcribe genes through a cycle of recruitment to promoter DNA, initiation, elongation, and termination. After termination, RNAP is thought to initiate the next round of transcription by detaching from DNA and rebinding a new promoter. Here we use single-molecule fluorescence microscopy to observe individual RNAP molecules after transcript release at a terminator. Following termination, RNAP almost always remains bound to DNA and sometimes exhibits one-dimensional sliding over thousands of basepairs. Unexpectedly, the DNA-bound RNAP often restarts transcription, usually in reverse direction, thus producing an antisense transcript. Furthermore, we report evidence of this secondary initiation in live cells, using genome-wide RNA sequencing. These findings reveal an alternative transcription cycle that allows RNAP to reinitiate without dissociating from DNA, which is likely to have important implications for gene regulation.