The discrete dynamical system is obtained by discretizing the solution cluster of ordinary differential equations. Due to the simple form and easy way of reflecting the nature of the problem， it has flourished since the 1960s under the initiative of Smale and other famous mathematicians. The study on n-th iteration of functions can help us understand long-term behaviors of the orbits of the discrete dynamical systems. There have been plentiful results on n-th iteration of the quadratic fractional functions.In this paper， based on the previous results， three kinds of unsolved cases are investigated by using the conjugation similarity method， i.e.， (I) b1=0 and a1c1=0； (II) b1≠0 and a1c1=0； (III) a1b1c1≠0 and a1=a2+1，b2=b1+2，c1=c2+1. The principle of conjugation similarity method is to find reversible bridge function to convert the quadratic fractional functions into quadratic functions, then， according to the existing n-th iteration results on quadratic functions， we can solve the problem. The key point of this method is to find bridge functions， but there is no general method. Thus， for every case, we will find different bridge functions.