A new empirical parametrization for the estimation of cross-sections of projectile fragments has been prescribed for studying the advantages and limitations of high energy RI beams for the production of new exotic nuclei. The parametrization reproduces the experimental data for the production of fragments from neutron rich projectiles accurately in contrast to the existing parametrization which tends to overestimate the cross-section of neutron rich fragments in most cases. The modified formalism has been used to compute the cross-sections of neutron-rich species produced by fragmentation of radioactive projectiles (RIBs). It has been found that, given any limit of production cross -section, the exoticity of the fragment increases rather slowly and shows a saturation tendency as the projectile is made more and more exotic.
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