  The effect of entanglement on off-diagonal geometric phases is investigated
in the paper. Two spin-1/2 particles in magnetic fields along the $y$ direction
are taken as an example. Three parameters (the purity of state $r$, the mixing
angle $\theta$ and the relative phase $\beta$) are chosen to characterize the
initial states. The nodal points at which the usual geometric phases disappear
are calculated and illustrated as a function of the three parameters.
