  We examine four dimensional magnetically charged extremal black holes in
certain non-linear U(1) gauge theories coupled to two derivative gravity. For a
given coupling, one can tune the magnetic charge (or vice versa) so that the
curvature singularity at the centre of the space-time is cancelled. Since these
solutions have a horizon but no singularity, they have been called regular
black holes. Contrary to recent claims in the literature, we find that the
entropy function formalism reproduces the near horizon geometry and gives the
correct entropy for these objects.
