We introduce a K-Spectral Centroïd algorithm, a variant of K-Means to cluster large time series. K-Spectral Centroïd uses a dissimilarity between time series, which is invariant re- garding translation and scaling. This algorithm is relatively expensive in computation time. Indeed, during the assignment phase, it requires testing all possible translations to identify the best solution. During the representation phase, the calculation of the new barycenter requires the extraction of the smallest eigenvalue of a matrix. We propose in this work to improve these two points. We measure subsequently the impact of these improvements on various experi- ments.