Among the clustering methods, K-Means and its variants are very popular. These methods solve at each iteration the first-order optimality conditions. However, in some cases, the function to be minimized is not convex, as for the Fuzzy C-Means version with Mahalanobis distance (FCM-GK). In this study, we apply the Alternating Directions Method of Multiplier (ADMM) to ensure a good convergence. ADMM is often applied to solve a separable convex minimization problem with linear constraints. ADMM is a decomposition/coordination method with a coordination step provided by Lagrange multipliers. By appropriately introducing auxiliary variables, this method allows the problem to be decomposed into easily solvable convex subproblems while keeping the same iterative structure. Numerical results have demonstrated the significant performance of the proposed method compared to the standard method, especially for high-dimensional data.