  The non-Markovian decoherence of quantum and classical correlations is
analytically obtained when two qubits are asymmetrically subjected to the bit
flip channel and phase flip channel. For one class of initial mixed states,
quantum correlations quantified by quantum discord decay synchronously with
classical correlations. The discovery that the decaying rates of quantum and
classical correlations suddenly change at the characteristic time is physically
interpreted by the distance from quantum state to the closest classical states.
In a large time interval, quantum correlations are greater than classical
correlations. The quantum and classical correlations can be preserved over a
longer period of time via the kernel characterizing the environment memory
effects.
