This paper deals with the study of global analysis of following $(1,2)-$type system of non-linear difference equations:\[ u_{n+1}=\frac{\alpha v_{n-1}}{\beta +\gamma v_{n}^{p}v_{n-2}^{q}},\ \ \ \ \ \ v_{n+1}=\frac{\alpha _{1}u_{n-1}}{\beta _{1}+\gamma _{1}u_{n}^{p}u_{n-2}^{q}},\ \ \ \ n=0,1,... \] where the parameters $\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1,}p,q$ and the initial conditions $u_{i},v_{i},$ $i=-2,-1,0$ are non negative real numbers.