Viral recombination has the potential to bring about viral genotypes with modified phenotypic characteristics, including transmissibility and virulence. Although the capacity for recombination among Betacoronaviruses is well documented, SARS-CoV-2 has only been circulating in humans for approximately 8 months and thus has had a relatively short window of opportunity for the occurrence of recombination. The ability to detect recombination has further been limited by the relatively low levels of genetic diversity in SARS-CoV-2. Despite this, two studies have reported recombinants among SARS-CoV-2 strains. Here we first revisit these findings with a new analysis approach, arguing that neither presents a clear case of within-SARS-CoV-2 recombination. Applying this same approach to available SARS-CoV-2 sequences, we then identify five recombinant genomes. Each of these genomes contain phylogenetic markers of two distinct SARS-CoV-2 clades. Further, the predicted parent clades of these recombinant genomes were, with one exception, documented to be co-circulating in the country of infection in the two weeks prior to the sample being collected. Our results indicate that recombination among SARS-CoV-2 strains is occurring, but is either not widespread or often remains undetectable given current levels of viral genetic diversity. Efforts to monitor the emergence of new recombinant genomes should therefore be sustained.