Abstract: I introduce the quaternionic geometry as a classical first-order G-structure on one hand and as an example of a parabolic geometry on the other hand. Then I show what its flat model looks like. In such flat case, there appears a family of non-standard differential operators of order four between differential forms. It turns out that these operators admit curved analogues between forms on an arbitrary manifold with a quaternionic structure. Finally, I briefly introduce the concept of strongly invariant operators and I sketch out the proof that the operators in question do not belong to them.