A converb is a form that consists of a °verb °stem and a special °affix but no °subject °person indexing and that can occur as the °predicate of a °subordinate clause that is neither a °relative clause nor a °complement clause.
The definition here is from Haspelmath (2027). It is different from the definition in (1995) in that it does not make reference to the notions "nonfinite" and "adverb" or "adverbial", and in that it does not rely on a "main function". Instead of "nonfinite", it specifies the presence of a special affix and the absence of subject person indexing.
converb (STR) = a deranked predicate form in an asyndetic deranked adverbial clause construction that lacks subject person indexation. Example: in Sitting in front of his desk, he noticed a bright light out the window, sitting is a converb. Haspelmath (1995: 5) excludes from the converb category forms that are deranked with subject person indexation that is different from that found with declarative main clause predication.