This paper proposed a new algorithm of Coupling from the Past (CFTP) with directional threshold. CFTP, also called Exact Sampling, established in 1996 by Propp and Wilson, aimed that it would eliminate the need to compute Markov chain convergence rate for the quality control. CFTP was used in mixture models of Monte Carlo and worked well in low computation complexity problems. The Coupling from the Past was appealing for its invariant structure but in many applications the process of coupling was not always an independent process. And this suboptimal algorithm would easily be trapped into local trap and its convergence was much affected. In this paper a new algorithm with directional threshold is presented and supported from simulation experiments; comparison of computing results with CFTP shows improvement of convergence out of the two sets of samples, with different total samples number respectively.