This paper studies the problem of discovering subsequences, known as motifs, that are common to a given collection of related biosequences, by proposing a greedy algorithm for learning a mixture of motifs model through likelihood maximization. The approach adds sequentially a new motif to a mixture model by performing a combined scheme of global and local search for appropriately initializing its parameters. In addition, a hierarchical partitioning scheme based on kd-trees is presented for partitioning the input dataset in order to speed-up the global searching procedure. The proposed method compares favorably over the well-known MEME approach and treats successfully several drawbacks of MEME.