f[x_]:=1/(1-x)
x0=0.321;
n=10;
nl=NestList[f,x0,n]

nl4=Transpose[{nl,nl,nl,nl}]//Flatten;

nl5=Take[nl4,{4,-4}];
nl6=Partition[nl5,2]

p1=ListPlot[nl6,Joined->True,PlotStyle->Red];
p2=Plot[{x,f[x]},{x,-4,4}];
Show[p2,p1]