Multi-point constraints are essential in modeling various engineering problems, e.g. in the context of joints undergoing large rotations, coupling of different element types in finite element analysis and considering periodic boundary conditions in FE² method. The master-slave elimination is an efficient method for the numerical treatment of the constraints because it reduces the dimension of the resulting linear system which is particularly advantageous when a large number of constraints have to be considered. However, the method requires an inversion of the submatrix of the constraint Jacobian. For nonlinear constraints, this inversion has to be performed at every single iteration step of the Newton-Raphson scheme [1]. Nevertheless, the method exhibits a priori a reduced computational complexity compared to Lagrange multipliers and the penalty method. This is also the case if the analysis of redundant constraints and the identification of slave degrees of freedom are included and the computation of the reduced row-echelon form replaces the inversion [2]. The aim of this talk is to present a method for drastically increasing the computational efficiency of this already efficient method. It is based on the exploitation of the specific structure of the constraint Jacobian as it appears in typical engineering applications. The analysis of this structure is twofold: First, small submatrices (constraint clusters) are identified. Second, the coupling type of each cluster is classified. Both steps are performed once during pre-processing without significant computational effort. All matrix operations required for this are performed using the CSR technique for storing sparse matrices, which is also particularly advantageous because all the matrices required for this are already stored in this format. The exploitation of the cluster structure allows the parallelization of computing the reduced row echelon form. This drastically reduces the computational cost. Finally, this parallelized computation is embedded in the master-slave elimination. The speed-up of this improved formulation over the previous master-slave elimination as well as other constraint methods is demonstrated using numerical examples. [1] Boungard & Wackerfuß: Master-slave elimination scheme for arbitrary smooth nonlinear multi-point constraints. Comp Mech, 74, 2024 [2] Boungard & Wackerfuß: Identification, elimination and handling of redundant nonlinear multi-point constraints. In preparation.