The radial local dynamics in poly(1,4-trans-butadiene) melts is studied using molecular dynamics simulations. In this work, the hopping peak is observed in the Van Hove space-time correlation function G(s)(r,t) for the first time in polymeric systems. The hopping motion, observed only for methine hydrogen, is also identified in the mean-square displacement and the intermediate scattering function F-s(k,t) through the relative dynamics of the hopping methine hydrogen and the nonhopping methylene hydrogen. The hopping motion is found to cause an unusual broadening of the dispersion width in the dynamic structure factor S-inc(k,omega). Active free volume is proposed in terms of G(s)(r,t) at a short time, which offers a consistency to the relationship between free volume and local dynamics. Fast counterrotation at a pair of CH=CH2 bonds across a CH=CH bond is found responsible for the hopping peak in this polymer, and a new hopping criterion modified for polymeric liquids is proposed.