We consider a situation where the density and peculiar velocities in real space are linear , and we calculate \xi _ { s } the two-point correlation function in redshift space , incorporating all non-linear effects which arise as a consequence of the map from real to redshift space .
Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space .
We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of \xi _ { s } .
While the deviations are insignificant for the monopole \xi _ { 0 } , the hexadecapole \xi _ { 4 } exhibits large deviations from the linear predictions .
For a COBE normalised \Gamma = 0.25 , h = 0.5 CDM power spectrum our results for \xi _ { 4 } deviate from the linear predictions by a factor of two at the scales \sim 10 h ^ { -1 } { Mpc } .
The deviations from the linear predictions depend separately on f ( \Omega ) and b .
This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only \beta = f ( \Omega ) / b .

We also show that the commonly used phenomenological model where the non-linear redshift two-point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function is a limiting case of our result .