  We investigate the transfer of entanglement from source particles (SP) to
target particles (TP) in the Heisenberg interaction $ H=\vec s_{1} \cdot \vec
s_{2}$. In our research, TP are two qubits and SP are two qubits or qutrits.
When TP are two qubits, we find that no matter what state the TP is initially
prepared in, at the specific time $t=\pi$, the entanglement of TP can attain to
1 after interaction with SP which stay on the maximally entangled state. For
the TP are two qutrits, we find that the maximal entanglement of TP after
interaction is relative to the initial state of TP and always cannot attain to
1 to almost all of initial states of TP. But we discuss an iterated operation
which can make the TP to the maximal entangled state.
