The \(k\)-means algorithm is one of the most widely used methods for solving the minimum sum-of-squares clustering (MSSC) problem, but it is well known to be sensitive to initialization and prone to convergence to poor local minima. In this work, we revisit the classical centroid update rule and propose a variant of \(k\)-means in which cluster centers are updated through a controlled movement toward their corresponding centroids. The proposed approach introduces a parameter that governs the magnitude of the update, allowing the algorithm to deviate from exact centroid updates while preserving the simplicity and computational efficiency of \(k\)-means. Computational experiments on benchmark datasets demonstrate that the proposed method consistently improves solution quality compared to standard \(k\)-means under equal computational budgets, achieving improvements of up to 15% without incurring additional computational overhead. These results suggest that strictly updating centers to centroids at every iteration is not always optimal from an algorithmic perspective, and that controlled update steps can lead to better clustering performance.