Major efficiency is an efficiency theory of multiobjective programming, whichis based on the law of majority. For the case that the feasible region is a finite set, paper [3] gave a comparison-number method for finding major efficient solutions and major optimalsolutions.This paper represents a new method to solve the same problem. The new method isbased on a concept of efficient equivalence point set. We give the definition of efficient equivalence point set, discuss the relationship between it and major efficiency, and present a new approach to find major efficient (optimal) solutions.