  In this paper, we study the bipartite entanglement of spin coherent states in
the case of pure and mixed states. By a proper choice of the subsystem spins,
the entanglement for large class of quantum systems is investigated. We
generalize the result to the case of bipartite mixed states using a simplified
expression of concurrence in Wootters' measure of the bipartite entanglement.
It is found that in some cases, the maximal entanglement of mixed states in the
context of $su(2)$ algebra can be detected. Our observations may have important
implications in exploiting these states in quantum information theory.
