  We study a Kitaev model on a square lattice, which describes topologically
trivial superconductor when gap opens, while supports topological gapless phase
when gap closes. The degeneracy points are characterized by two vortices in
momentum space, with opposite winding numbers, which are not removable unless
meet together. We show rigorously that the topological gapless phase always
hosts a partial Majorana flat band edge modes in a ribbon geometry, although
such a single band model has zero Chern number as a topologically trivial
superconductor. The flat band disappears when the gapless phase becomes
topologically trivial, associating with the mergence of two vortices. Numerical
simulation indicates that the flat band is robust against the disorder. This
finding indicates that the bulk-edge correspondence can be extended to
superconductors in the topologically trivial regime as recently proposed in
Ref. [PRL 118, 147003 (2017)].
