In an earlier communication we have developed a recursion based approach to the study of phase stability and transition of binary alloys [K. Tarafder, M. Rahaman, D. Paudyal, B. Sanyal, O. Eriksson, A. Mookerjee, Physica B 403 (2000) 4111]. We had combined the recursion method introduced by Haydock et al. [J. Phys. C Solid State Phys. 5 (1972) 2485] and the our augmented space approach [A. Mookerjee, J. Phys. C Solid State Phys. 6 (1973) 1340] with the orbital peeling technique proposed by Burke [Surf. Sci. 58 (1976) 349] to determine the small energy differences involved in the discussion of phase stability. We extend that methodology for the study of MnCr alloys.