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Consider an immersed Legendrian surface in the five dimensional complexprojective space equipped with the standard homogeneous contact structure. Weintroduce a class of fourth order projective Legendrian deformation called\emph{$\,\Psi$-deformation}, and give a differential geometric characterizationof surfaces admitting maximum three parameter family of such deformations. Twoexplicit examples of maximally $\, \Psi$-deformable surfaces are constructed;the first one is given by a Legendrian map from $\, \PP^2$ blown up at threedistinct collinear points, which is an embedding away from the -2-curve anddegenerates to a point along the -2-curve. The second one is a Legendrianembedding of the degree 6 del Pezzo surface, $\, \PP^2$ blown up at threenon-collinear points. In both cases, the Legendrian map is given by a system ofcubics through the three points, which is a subsystem of the anti-canonicalsystem.

Projectively deformable Legendrian surfaces