  It is shown that a 4-recollement of derived categories of CM-finite algebras
induces a 2-recollement of the corresponding Cohen-Macaulay Auslander algebras,
which generalises the main theorem of Pan [S. Y. Pan, Derived equivalences for
Cohen-Macaulay Auslander algebras, J. Pure Appl. Algebra 216 (2012), 355{363].
Moreover, both Auslander- Reiten conjecture and Gorenstein projective
conjecture are shown invariant under 3 (or 4)-recollement of unbounded derived
categories of algebras.
