  Darboux Wronskian formulas allow to construct Darboux transformations, but
Laplace transformations, which are Darboux transformations of order one cannot
be represented this way. It has been a long standing problem on what are other
exceptions. In our previous work we proved that among transformations of total
order one there are no other exceptions. Here we prove that for transformations
of total order two there are no exceptions at all. We also obtain a simple
explicit invariant description of all possible Darboux Transformations of total
order two.
