Translation:The bank doesn't accept a single check without a signature.
Why "without a signature"? There is no need for an article, it's without whatsoever signature. And Google Books site shows almost equal usage of "without signature" and "without the signature" while "without a signature" is less frequent. Anyway, if one still wants an article that would be more logical to use "the" as we need the authentic signature of the cheque drawer, not any.