The local motions of bulk amorphous polybutadienes (PBDs) have been studied by a molecular dynamics simulation. Fully atomistic models of PBDs have been obtained at a realistic bulk density under periodic boundary conditions. Local chain motions are examined for poly(cis-1,4-butadiene) (cis-PBD) and poly(trans-1,4-butadiene) (trans-PBD) well above the glass transition temperature, where the only structural difference is imposed by the different conformational states at the double bond. The local motions are found to be strikingly different in the two polymers. Intramolecular cooperative conformational transitions occur at second-neighbor bond pairs of CH-CH, in both PBDs. In trans-PBD, both CH2-CH2 and CH=CH triplets undergo cooperative counterrotations. In cis-PBD, CH2-CH2 triplets undergo counterrotations while CH=CH triplets undergo corotations. Intermolecular cooperativity, probed by the local free volume, has Little influence on local relaxation processes. The effect of libration on the shape of autocorrelation functions (ACFs) is significant over the entire time range. A universality is found in the time evolution of the Kohlrausch-Williams-Watts exponent regardless of the type and order of the ACF. On the other hand, the single exponential decay regarded as common at short times is only due to the discreteness of conformational states.