  By examining organic conductor alpha-(BEDT-TTF)_2I_3 which is described by a
nearest neighbors tight-binding model it is shown that because of inversion
symmetry, each component of a wave function (WF) exhibits nodal lines (NLs) in
the Brillouin zone. In the absence of any band crossing, each NL connects two
time reversal invariant momenta (TRIM) as partners. In the presence of a pair
of Dirac points (band crossing), for each band that crosses and for each WF
component there is a NL that connects the pair of Dirac points via a TRIM
without partner. This second kind of NL leads to a discontinuous sign change
for non vanishing components of the WF. Such a property is at the origin of the
+/- pi Berry phase accumulated on a contour integral encircling one Dirac
point. The results are examplified by numerical calculation of WFs components
for the above conductor with a 3/4 filled band.
