Abstract: A classification in terms of accuracy of flux limited high resolution schemes in steep gradient region is done based on two different total variation (TV) stability region. The dependence of TV stability region on the smoothness parameter is discussed which relates these two TV stability regions. A common unifying TV stability region is proposed for both class of schemes. Moreover new flux limiters, satisfying the unifying TV stability region are also proposed which are robust and work efficiently for both backward (left) and forward (right) moving solution profile. Main significant feature of this work is that it can improve accuracy of all existing flux limiters based schemes. Numerical results on linear test problems are given to support the theoretical discussion.