  We consider an entangled but non-interacting qubit pair a_{1} and b_{1} that
are independently coupled to a set of local qubit systems, a_{I} and b_{J}, of
0-bit value, respectively. We derive rules for the transfer of entanglement
from the pair a_{1}-b_{1} to an arbitrary pair a_{I}-b_{J}, for the case of
qubit-number conserving local interactions. It is shown that the transfer rule
depends strongly on the initial entangled state. If the initial entanglement is
in the form of the Bell state corresponding to anti-correlated qubits, the sum
of the square of the non-local pairwise concurrences is conserved. If the
initial state is the Bell state with correlated qubits, this sum can be
reduced, even to zero in some cases, to reveal a complete and abrupt loss of
all non-local pairwise entanglement. We also identify that for the nonlocal
bipartitions A-b_{J} involving all qubits at one location, with one qubit b_{J}
at the other location, the concurrences satisfies a simple addition rule for
both cases of the Bell states, that the sum of the square of the nonlocal
concurrences is conserved.
