Almost all the coupled electron pair approximation (CEPA)-like developments based on multi-reference functions do not satisfy invariance with respect to separate unitary transformation among doubly occupied, active and virtual orbitals. Those, which do satisfy this criterion, use empirical CEPA-like corrections involving suitably averaged pair-correlation terms. We develop in this Letter a CEPA-like approximant to the state-specific multi-reference coupled cluster (SS-MRCC) formalism [J. Chem. Phys. 100, (1999) 6171] which includes all the exclusion principle violating terms rigorously, and display manifest orbital-invariance. The theory, termed as SS-MRCEPA(I), is also rigorously size-extensive, size-consistent and bypasses intruders in a natural manner. (C) 2004 Elsevier B.V. All rights reserved.