Despite their importance in a wide range of living organisms, self-cleaving ribozymes in the human genome are few and poorly studied. Here, we performed deep mutational scanning and covariance analysis of two previously proposed self-cleaving ribozymes (LINE-1 and OR4K15). We found that the regions essential for ribozyme activities are made of two short segments, with a total of 35 and 31 nucleotides only. The discovery makes them the simplest known self-cleaving ribozymes. Moreover, the essential regions are circular permutated with two nearly identical catalytic internal loops, supported by two stems of different lengths. These two self-cleaving ribozymes, which shape like lanterns, are similar to the catalytic regions of the twister sister ribozymes in terms of sequence and secondary structure. However, the nucleotides at the cleavage site have shown that mutational effects on the two twister sister-like (TS-like) ribozymes are different from the twister sister ribozyme. The discovery of TS-like ribozymes reveals a ribozyme class with the simplest and, perhaps, the most primitive structure needed for self-cleavage.