We present a new algorithm for solving the two-set split common fixed point problem with total quasi-asymptotically pseudocontractive operators and consider the case of quasi-pseudocontractive operators.Under some appropriate conditions, we prove Lounge Chairs that the proposed algorithms have strong convergence.The results presented in this paper improve and extend the previous algorithms and results of Censor and Segal (2009), Moudafi (2011 and 2010), Mohammed (2013), Yang et al.(2011), PROMASIL VANILLA Chang et al.(2012), and others.