  From the group theoretical ground, the Blount's theorem prohibits the
existence of line nodes for odd-parity superconductors (SCs) in the presence of
spin-orbit coupling (SOC). We study the topological stability of line nodes
under inversion symmetry. From the topological point of view, we renovate the
stability condition of line nodes, in which we not only generalize the original
statement, but also establish the relation to zero-energy surface flat
dispersions. The topological instability of line nodes in odd-parity SCs
implies not the absence of bulk line nodes but the disappearance of the
corresponding zero-energy surface flat dispersions due to surface Rashba SOC,
which gives an experimental means to distinguish line nodes in odd-parity SCs
from those in other SCs.
