  The non-Markovian dynamics of quantum entanglement is studied by the
Shabani-Lidar master equation when one of entangled quantum systems is coupled
to a local reservoir with memory effects. The completely positive reduced
dynamical map can be constructed in the Kraus representation. Quantum
entanglement decays more slowly in the non-Markovian environment. The
decoherence time for quantum entanglement can be markedly increased by the
change of the memory kernel. It is found out that the entanglement sudden death
between quantum systems and entanglement sudden birth between the system and
reservoir occur at different instants.
