  We study N=2 supergravity deformed by a genuine supersymmetric completion of
the $\lambda R^4$ term, using the underlying off shell N=2 superconformal
framework. The gauge-fixed superconformal model has unbroken local
supersymmetry of N=2 supergravity with higher derivative deformation.
Elimination of auxiliary fields leads to the deformation of the supersymmetry
rules as well as to the deformation of the action, which becomes a Born-Infeld
with higher derivative type action. We find that the gravitino supersymmetry
deformation starts from $\lambda \, \pa^4 {\cal F}^3$ and has higher
graviphoton couplings. In the action there are terms $\lambda^2 \pa^8 {\cal
F}^{6}$ and higher, in addition to original on shell counterterm deformation.
These deformations are absent in the on shell superspace and in the candidate
on shell counterterms of N=4,~8 supergravities, truncated down to N=2. We
conclude therefore that the undeformed on shell superspace candidate
counterterms break the N=2 part of local supersymmetry.
