MicroRNA-offset-RNAs (moRNAs) were recently detected as highly abundant class of small RNAs in a basal chordate. Using short read sequencing data, we show here that moRNAs are also produced from human microRNA precursors, albeit at quite low expression levels. The expression levels of moRNAs are unrelated to those of the associated microRNAs. Surprisingly, microRNA precursors that also show moRNAs are typically evolutionarily old, comprising more than half of the microRNA families that were present in early Bilateria, while evidence for moRNAs was found only for a relative small fraction of microRNA families of recent origin.