Clustering is a data mining problem that has received significant attention by the database community. Data set size, dimensionality and sparsity have been identified as aspects that make clustering more difficult. This work introduces a fast algorithm to cluster large binary data sets where data points have high dimensionality and most o their coordinates are zero. This is the case with basket data transactions containing items, that can be represented as sparse binary vectors with very high dimensionality. An experimental section shows performance, advantages and limitations of the proposed approach.