A formally exact partitioning of the MRCISDTQ Hamiltonian for multiple electronic states to form a Hermitian effective Hamiltonian of the dimension of the MRCISD space is presented. From this partitioned form, a computationally amenable approximation can be made that leads to a new method for which the name nR-MRCISD(TQ) is suggested. nR-MRCISD(TQ) includes the single-state MRCISD-Bk and MRCISD(TQ) methods as particular cases. In addition, new formulas for Davidson-type energy corrections for one MRCISD state at a time have been obtained, which are not more computationally expensive but both theoretically and practically more accurate than the traditional ones. (C) 2010 Elsevier B. V. All rights reserved.