  We propose an effective Hamiltonian approach to investigate decoherence of a
quantum system in a non-Markovian reservoir, naturally imposing the complete
positivity on the reduced dynamics of the system. The formalism is based on the
notion of an effective reservoir, i.e., certain collective degrees of freedom
in the reservoir that are responsible for the decoherence. As examples for
completely positive decoherence, we present three typical decoherence processes
for a qubit such as dephasing, depolarizing, and amplitude-damping. The effects
of the non-Markovian decoherence are compared to the Markovian decoherence.
