The DNA-binding protein PRDM9 has a critical role in specifying meiotic recombination hotspots in mice and apes, but it appears to be absent from other vertebrate species, including birds. To study the evolution and determinants of recombination in species lacking the gene that encodes PRDM9, we inferred fine-scale genetic maps from population resequencing data for two bird species: the zebra finch, Taeniopygia guttata, and the long-tailed finch, Poephila acuticauda. We found that both species have recombination hotspots, which are enriched near functional genomic elements. Unlike in mice and apes, most hotspots are shared between the two species, and their conservation seems to extend over tens of millions of years. These observations suggest that in the absence of PRDM9, recombination targets functional features that both enable access to the genome and constrain its evolution.