This paper introduces a new multi-label classifier based on Boolean matrix decomposition. Boolean matrix decomposition is used to extract, from the full label matrix, latent labels representing useful Boolean combinations of the original labels. Base level models predict latent labels, which are subsequently transformed into the actual labels by Boolean matrix multiplication with the second matrix from the decomposition. The new method is tested on six publicly available datasets with varying numbers of labels. The experimental evaluation shows that the new method works particularly well on datasets with a large number of labels and strong dependencies among them.