The thing is though - if no one understands the existing system, how could you ever hope to build a new one that provides the same functionality? You'll have to interrogate that system to find out how it functions in order to replicate it. I find that this is often easier done by incremental refactorings of the legacy codebase (And writing a test harness in the process). So the rewrite really becomes a mission of analysing/documentation.

However messy it may be, there's usually a lot of domain knowledge to be learned from such a legacy codebase.