We have studied the local structure of a Ba(Fe1-xCox)(2)As-2 superconductor using temperature dependent extended X-ray absorption fine structure (EXAFS) measurements. Polarized EXAFS at the Fe K-edge on an optimally doped (x = 0.06) single crystal has permitted us to determine atomic displacements across the superconducting transition temperature (T-c). The Fe-As bondlength hardly shows any change with temperature; however, the Fe-Fe sublattice reveals a sharp anomaly across T-c, indicated by a significant drop in mean square relative displacements, similar to the one known for cuprates and A15-type superconductors. We have also found a large atomic disorder around the substituted Co, revealed by polarized Co K-edge EXAFS measurements. The Co-Fe/Co bonds are more flexible than the Fe-Fe bonds with the As-height in Co-containing tetrahedra being larger than the one in FeAs4. The results suggest that the local Fe-Fe bondlength fluctuations and the atomic disorder in this sub-lattice should have some important role in the superconductivity of Ba(Fe1-xCox)(2)As-2 pnictides.