  We demonstrate that Majorana fermions exist in edges of systems and in a
vortex core even for superconductors with nodal excitations such as the d-wave
pairing state under a particular but realistic condition in the case with an
anti-symmetric spin-orbit interaction and a nonzero magnetic field below the
upper critical field. We clarify that the Majorana fermion state is
topologically protected in spite of the presence of bulk gapless nodal
excitations, because of the existence of a nontrivial topological number. Our
finding drastically enlarges target systems where we can explore the Majorana
fermion state.
