A new method namely, separation and bound method is proposed to find an optimal intuitionistic fuzzy (IF) solution to fully intuitionistic fuzzy linear programming (IFLP) problems, in which ranking functions are not used. The proposed method is based on the crisp linear programming (LP) technique. In the optimal solution of the fully IFLP problem obtained by the proposed method, the values of the decision variables do not contain any negative part. Separation and bound method is an appropriate method to apply for finding an optimal solution of IFLP problems occurring in real life situations. © Research India Publications.