  We prove a geometrical version of Herbert's theorem by considering the
self-intersection immersions of a self-transverse immersion up to bordism. This
generalises Herbert's theorem to additional cohomology theories and gives a
commutative diagram in the homotopy of Thom complexes. The proof uses Koschorke
and Sanderson's operations and the fact that bordism of immersions gives a
functor on the category of smooth manifolds and immersions.
