An investigation on the effect of practically possible upper and lower parabolic dips in the refractive index profile of the inner core of the coaxial fiber Raman gain amplifier is reported using matrix method for single pump. It is seen that for lower parabolic dip, the tolerable limits of dip parameters correspond to dip depth of 0.25% and dip width of 25% of the respective parameters for ideal step index profile case and agree with the earlier predicted linear dip. However, for upper parabolic dip, one gets higher gain and better flatness at these limits. Even up to 1% of the dip depth for 25% of dip width or 75% of dip width for 0.25% of the dip depth or 0.5% of dip depth and 50% of dip width, one can expect performance as good as that of the ideal one. However, since system designers will be aimed to produce ideal profile, our recommendation is to keep tolerable limits within 0.25% of dip depth and 25% of dip width of respective parameters. But one can accept profile with upper parabolic dip if there is deviation within the above relaxation limits for such dip.