  In this note we study the puzzle posed by two M5-branes intersecting on a
string (or equivalently, a single M5-brane wrapping a holomorphic four-cycle in
C^4). It has been known for a while that this system is different from all
other configurations built using self-intersecting M-branes; in particular the
corresponding supergravity solution exhibits various curious features which
have remained unexplained. We propose that the resolution to these puzzles lies
in the existence of a non-zero two-form on the M5-brane world-volume.
