The strict complementary slackness condition (SCSC) is an important concept in the duality theory of linear programming (LP). The current study aims at extending this concept to the framework of linear fractional programming (LFP). First, we define this concept in this framework and demonstrate the existence of a strict complementary solution - a pair of primal and dual optimal solutions satisfying the SCSC. Second, we show that the problem of finding such a solution reduces to that of identifying a relative interior point of a polyhedron. More recently, Mehdiloozad et al. (2016) have addressed the latter problem by proposing an LP problem. Using their proposed LP problem, we finally develop two procedures for finding a strict complementary solution.