We present an efficient algorithm for relativistic exact-decoupling[1] calculations.Spin-orbit coupling is taken into account for the evaluation of relativistically transformed Hamiltonian.As the relativistic decoupling transformation has to be evaluated with primitive functions,the construction of the relativistic one-electron Hamiltonian becomes the bottleneck of the whole calculation for large molecules.For the established exact-decoupling protocols,a minimal matrix operation count is established and discussed in detail.Furthermore,we apply our recently developed local DLU scheme[2] to accelerate this step.Its computational scaling can be reduced to linear scaling by employing the neighboring-atomic-blocks approximation.If a large molecule contains many light atoms,the computational costs can be further reduced by employing a well-defined non-relativistic approximation for these light atoms without significant loss of accuracy.With our new implementation two-component relativistic density functional calculations can be performed invoking the resolution-of-identity density-fitting approximation and point group symmetry to accelerate both the exact-decoupling and the two-electron part.The capability of our implementation is illustrated at the example of silver clusters with up to 309 atoms,for which the cohesive energy is calculated and extrapolated to the bulk.