Replicating circular RNAs are independent plant pathogens known as viroids, or act to modulate the pathogenesis of plant and animal viruses as their satellite RNAs. The rate of discovery of these subviral pathogens was low over the past 40 years because the classical approaches are technical demanding and time-consuming. We previously described an approach for homology-independent discovery of replicating circular RNAs by analysing the total small RNA populations from samples of diseased tissues with a computational program known as progressive filtering of overlapping small RNAs (PFOR). However, PFOR written in PERL language is extremely slow and is unable to discover those subviral pathogens that do not trigger in vivo accumulation of extensively overlapping small RNAs. Moreover, PFOR is yet to identify a new viroid capable of initiating independent infection. Here we report the development of PFOR2 that adopted parallel programming in the C++ language and was 3 to 8 times faster than PFOR. A new computational program was further developed and incorporated into PFOR2 to allow the identification of circular RNAs by deep sequencing of long RNAs instead of small RNAs. PFOR2 analysis of the small RNA libraries from grapevine and apple plants led to the discovery of Grapevine latent viroid (GLVd) and Apple hammerhead viroid-like RNA (AHVd-like RNA), respectively. GLVd was proposed as a new species in the genus Apscaviroid, because it contained the typical structural elements found in this group of viroids and initiated independent infection in grapevine seedlings. AHVd-like RNA encoded a biologically active hammerhead ribozyme in both polarities, and was not specifically associated with any of the viruses found in apple plants. We propose that these computational algorithms have the potential to discover novel circular RNAs in plants, invertebrates and vertebrates regardless of whether they replicate and/or induce the in vivo accumulation of small RNAs.