Near the conical intersection for the 1,2 (2)A' states of H-3 the derivativ
e coupling vector is calculated and analyzed on the plane of internal coord
inates, (U,V) or its polar coordinates (S, theta), based on the squares of
the internuclear distances. It is shown that in the vicinity of the conical
intersection the derivative coupling vector behaves like theta /2S, which
is responsible for the sign changes of the real-valued electronic wave func
tion when the nuclear configuration traverses a closed path enclosing a con
ical intersection. The analytic property of the wave functions is studied a
nd especially the observation of the sign change in the configuration state
function (CSF) coefficients of the real-valued electronic wave functions i
s demonstrated.