Molecular-dynamics simulations are performed to analyze the local chain dynamics of cis-1,4-polyisoprene at various temperatures. The volumetric glass transition was found at around 247 K. The torsional angle autocorrelation functions (TACF) for the three kinds of backbone chain and the orientation autocorrelation functions (OACF) for bond vectors in skeletal and side chain were analyzed both near the chain ends and in the middle of the chain. Various types of cooperative conformational jumps (and librations) were found in the melt chain. However, the cooperative counter-rotation at second-neighbor single bond pairs, HC-CH2 and CH2-C, became a major correlation as the temperature decreased to the subglass region. Even in the subglass chain at 173 K, more than 30% bond pairs showed cooperative counter-rotation at the second-neighbor (Group A) under the conditions in which about 60% of the bond pairs showed no conformational jump (Group B) during 20 ns molecular dynamics (MD) runs. The TACF decays for the torsions in Group A were highly different from those in Group B. In contrast, the OACF decays for the classified C-CH3 vectors next to Group A showed no difference from that next to Group B. These findings indicated that the cooperative transitions at the second-neighbor were only a short-range correlation on the single bond pairs without changing the reorientation of the two double bond planes next to the single bond pairs.