On this PES, the dashed red NT does not find the next minimum after SP2, but continues uphill to the maximum, an SP of index two, with two negative eigenvalues of the Hessian matrix. This is allowed by the property of regular NTs. They connect stationary points with an index difference of one . Here the NT moves from index one of SP2 to index two of the maximum. Note that saddles of index two have been discussed in chemistry since 1986 . Currently they play a role in the discussion about roaming atoms .