  Through the quantum trajectory approach, we calculate the geometric phase
acquired by a bipartite system subjected to decoherence. The subsystems that
compose the bipartite system interact with each other, and then are entangled
in the evolution. The geometric phase due to the quantum jump for both the
bipartite system and its subsystems are calculated and analyzed. As an example,
we present two coupled spin-$\frac 1 2 $ particles to detail the calculations.
