Let u be a mapping from a bounded domain S ⊂ R 4 into a compact Riemannian manifold N . Its intrinsic biharmonic energy E 2 (u) is given by the squared L 2 -norm of the intrinsic Hessian of u. We consider weakly converging sequences of critical points of E 2 . Our main result is that the energy dissipation along such a sequence is fully due to energy concentration on a finite set and that the dissipated energy equals a sum over the energies of finitely many entire critical points of E 2 .